Washington CNN  — 

Israeli Prime Minister Benjamin Netanyahu will face voters on Tuesday, just two weeks after he took a major political gamble by giving a controversial speech to the U.S. Congress against the Obama administration’s wishes.

The White House, clearly angered by an address criticizing its Iran deal-making, denied Netanyahu an Oval Office meeting during the visit. The reason, according to an official statement, was to “avoid the appearance of influencing a democratic election in a foreign country.”

Snubbing an Israeli prime minister, though, can influence Israeli voters as much as giving him a West Wing photo-op. And with U.S.-Israel tensions at a peak, many in Washington see telltale signs of an effort to oust a leader standing in the way of the Obama administration’s Middle East policies.

“This election cycle in Israel fits the hallmark of an American administration that seeks to influence the outcome,” said David Weinberg, a senior fellow at the Foundation for Defense of Democracies who has studied American influence in Israeli elections.

The White House denied it was attempting to influence the Israeli elections by rebuffing Netanyahu and pointed to the well-circulated statement on why the prime minister wasn’t offered a meeting: “As a matter of long-standing practice and principle, we do not see heads of state or candidates in close proximity to their elections.”

U.S. snubs Netanayhu before vote, again

But such visits – or the lack thereof – have historically been one of the diplomatic weapons U.S. administrations have deployed to sway the Israeli public.

Less than a month before the 1996 Israeli elections, President Bill Clinton organized the signing of an anti-terror pact before the cameras with Shimon Peres, the Labor Party prime minister whom Netanyahu ended up defeating for his first term in office. In 1999, Clinton similarly pursued what some call “snub diplomacy” when his administration denied Netanyahu meetings amidst a tight race with Labor’s Ehud Barak, to whom Netanyahu ultimately lost.

READ: Obama and Netanyahu: A clash of world views, not just personalities

The state of the “special relationship” with the United States is of crucial importance to Israeli voters, who see America as their closest and most important ally. So in risking a rupture with the White House, Netanyahu is also risking a break with Israeli voters.

“Traditionally, the Israeli public has been very sensitive to how the relationship is going and how well the Israeli leadership is managing that relationship,” said Daniel Kurtzer, a former U.S. ambassador to Israel.

But Netanyahu’s move to address Congress on Iran, a top concern for the Israeli public, was also seen as a bid to boost his electoral appeal by reinforcing that he is a leader on the world stage and will do everything he can to protect Israel. When Republican House Speaker John Boehner extended the invitation to Netanyahu, many jumped on the House leader for helping the prime minister politically. This week, footage of Netanyahu being warmly received on Capitol Hill made it into a campaign ad.

The partisan nature of the invitation and that it was done without White House coordination – Boehner is a chief Obama rival and disagrees emphatically with his Iran policy – heightened Democratic pique over Netanyahu’s appearance.

A dispute gets personal

Previous presidents have bristled at the hawkish, unflinching posture – especially when it comes to the Israeli-Palestinian peace process – that Netanyahu and other Likud party leaders have often struck. But the current antagonism, exacerbated by the speech, has become particularly personal.

Obama himself dismissed Netanyahu’s speech as “theater” and slammed his Israeli counterpart for offering “nothing new.” And a host of officials offered further criticism, including National Security Adviser Susan Rice, who called Netanyahu’s address “destructive” to the U.S-Israeli relationship.

READ: Bad relationship gets worse for Obama, Netanyahu

Netanyahu’s allies deny a political motive to the speech and have maintained that the hit to U.S.-Israeli ties was necessary because of the existential danger posed by Iran and fears that negotiations on its nuclear program would lead to a disastrous agreement as they reach a key deadline.

Former State Department official Aaron David Miller said the Obama administration is now sending “certain unmistakable signals” that Netanyahu isn’t the right prime minister to manage the U.S.-Israel relationship.

Miller witnessed the sending of similar signals in 1996 as one of the top officials coordinating Arab-Israeli negotiations in the Clinton administration.

‘We wanted Peres to win’

“We clearly had our favorites and we wanted Peres to win,” Miller recounted.

It hasn’t just been Netanyahu whom U.S. presidents have opposed. In the run-up to the 1992 Israeli elections that eventually saw Labor’s Yitzhak Rabin elected, George H.W. Bush tied up American loan guarantees to punish the right-wing Israeli government and pressure it to change its policy on settlements.

“[The idea] that we don’t intercede in Israeli politics is as foolish an assumption as that they don’t interfere in ours,” Miller said.

One of many developments seen as souring the Obama-Netanyahu relationship was the widespread accusation that the prime minister all but endorsed Republican presidential nominee Mitt Romney in his campaign to unseat Obama in 2012.

But just as Netanyahu – if he indeed tried – was unsuccessful in swaying that election, American presidents have also come up short.

There’s no clear indication right now that Netanyahu will be hurt by the U.S.-Israel row come Election Day. Netanyahu’s party saw a modest boost in one poll after Netanyahu’s speech to Congress. Several polls in recent days, however, suggest leading opposition party Zionist Union is gaining momentum in the wake of Netanyahu’s American saga. And the large number of undecideds and polling see-sawing throughout the race leave the final result very much in question.

Zionist Union leader Isaac Herzog has been taking every opportunity to use Netanyahu’s frayed ties with the U.S. administration against him.

‘Israel is isolated’

“The painful truth is that after all the applause, Netanyahu is alone and Israel is isolated,” Herzog said after Netanyahu’s speech to Congress.

But there are other issues – such as economic woes and questions about Israel’s security – that are also spelling trouble for Netanyahu.

And for all those alienated from Netanyahu’s Likud party by the breach with the United States, there are many in Israel who could reward him for it. Israelis have been mistrustful of Obama and have disliked many of his Middle East positions. Some believe being seen as standing up to the U.S. president will work in the prime minister’s favor.

READ: Netanyahu warns Congress: Deal will lead to Iranian nuclear bomb

“I think the people of Israel understand that the prime minister is representing our needs,” said Danny Danon, a Likud Knesset member. “I don’t think criticism from the administration will affect them.”

And while Netanyahu faces condemnation from the Obama administration and top Democratic officials, he’s also enjoying widespread praise from Republicans. The White House may have panned Netanyahu’s speech, but on Capitol Hill, the prime minister got standing ovations reminiscent of State of the Union addresses.

Zalman Shoval, a former ambassador to the U.S. and Netanyahu confidant, said the lack of uniform condemnation and public wariness about Obama could cancel out any loss of support due to U.S.-Israel tensions.

“It’s very difficult to gauge how much of an influence any sort of statement or implication or whatever insinuation can really have on the election battle here,” he said.

Several Israeli lawmakers – on both sides of the aisle – doubted whether the Obama administration was actively trying to influence the election.

An unprecedented visit

A skeptical Danon was joined by Labor’s Nachman Shai. He said that U.S. officials had simply “reacted and responded” to the “unprecedented” nature of Netanyahu’s visit.

Erel Margalit, another Labor Knesset member, agreed. “The administration responded to what was a frontal attack on its strategy in a way that was unprecedented.”

He added, however, “Let’s distinguish between two things: What they want in their heart and what they’re doing.”

Obama’s unpopularity is part of the reason Netanyahu’s opponents on the left are careful not to play up any White House role in the elections. And Netanyahu and his allies are cautious not to reinforce the notion of a rift or go on the offensive against an administration they hope to mend relations with if Netanyahu is reelected.

READ: 58 members of Congress skipped Netanyahu’s speech

The Netanyahu campaign wouldn’t comment on whether the White House was trying to unseat the prime minister. But in the media, the candidate has lashed out at a “worldwide effort” to remove him from office.

Aides explained his remarks as referring to a campaign aiming to change the government. One Netanyahu campaign official said money was coming from “every corner of the Earth.”

American consults show up in Israel

That effort’s being led by V15, a grassroots progressive movement with Obama campaign field director Jeremy Bird as a leading consultant.

Bird is just the latest in a long line of American political operatives and pollsters who have traveled across the ocean to help Israeli politicians.

Democratic consultants James Carville and Stanley Greenberg helped Barak in 1999, and Democratic veteran Paul Begala (who is also a CNN analyst) is now aiding Herzog. On the Republican side, digital strategist Vincent Harris, who now works for Sen. Rand Paul, signed up to help Netanyahu’s campaign this year.

Prominent Republican donors have also offered him support, perhaps no one more so than Sheldon Adelson. Adelson, the American casino magnate who spent more than $200 million backing Republicans in the 2012 presidential election, launched an Israeli newspaper, “Israel Today,” that vocally supports Netanyahu.

Distributed in the street and at train stations, the newspaper is free and has become the most-read in Israel.

Adelson was also present as Netanyahu delivered his address to Congress. His support is yet another reason some Democrats in Washington are less than fond of the prime minister.

While the Obama administration may not be leading an overt effort to undermine Netanyahu, Miller, the former State Department official, said there’s no doubt “corks will be popping at the White House and State Department if Netanyahu loses.”

Labott contributed reporting from Jerusalem.