Congressional Republicans are promising to continue aggressively challenging President Obama’s efforts to reach a nuclear deal with Iran despite confronting developments abroad and political disagreements at home that could complicate their strategy.

They are not second-guessing the decision to invite Israeli Prime Minister Benjamin Netanyahu to address Congress earlier his month. Netanyahu is at risk of losing a bid for reelection in a parliamentary vote Tuesday.

Meanwhile, the domestic political fallout from a controversial letter from Sen. Tom Cotton (R-Ark.) to Iranian leaders hasn’t deterred Republicans from taking a hard stance against Obama.

As voters in Israel cast ballots, some Republicans are openly pulling for Netanyahu, a national security hawk aligned with their views. Others are staying studiously neutral.

“I’m obviously hoping and praying that Netanyahu can pull it off,” said Rep. Marlin Stutzman (R-Ind.).

Sen. John McCain (R-Ariz.) said he is “not taking sides in that. That’s up to the Israeli people. I will honor whatever decision they make.”

Sen. Dan Coats (R-Ind.) said that what is happening in Israel “adds a layer of confusion to the negotiations going on in Iran.”

Republicans said they do not regret their decision to invite Netanyahu to speak to Congress. The invitation from Republican leaders was considered a broadside against Obama.

Rep. Tom Cole (R-Okla.), a close ally of House Republican leaders, said a Netanyahu loss would not reflect poorly on Republicans.

“I think if he loses, it’s going to be largely over domestic issues,” said Cole, who later added, “I don't think the Netanyahu visit hurt us very much.”

Recent polling showed Netanyahu and his Likud party facing a stiff challenge from Isaac Herzog, leader of the center-left Labor Party.

The Obama administration and five other world powers have been in talks with Iran with the hopes of limiting its nuclear program and ensuring that it does not produce a nuclear weapon. If Iran meets certain conditions, the United States and others are prepared to ease economic sanctions.

Republicans and some Democrats wary of Iran’s intentions want Congress to have more say on the international talks, which are up against a self-imposed deadline later this month.

There has been some disagreement in Republican circles about the usefulness of the Iran letter written by Cotton and signed by 46 of his GOP colleagues, with even some arguing that it could diminish the odds of forming a bipartisan coalition.

Despite the grumbling, congressional Republicans are not calling for the letter to serve as a signal that the party should pump the brakes on their Iran strategy.

Cotton, a freshman senator, warned Iranian leaders in his letter last week that any lasting nuclear deal must win the approval of not just Obama, but Congress as well. He also threatened that such a deal could be quickly voided once Obama leaves office.

Rep. Lee Zeldin (R-N.Y.) said it was “unfortunate” that the substance of Cotton’s letter was upstaged by the controversy over his decision to address it to Iran’s leaders. But Zeldin said that he would have signed the letter and that he doesn’t think Republicans should ease up on their fight against Obama.

“As long as the president continues to pursue a policy that is against the best interest of America and our allies, the attempts by everyone else in our country who sees through it is going to continue to get stronger and louder,” said Zeldin, the only Jewish Republican member of Congress.

No Democrats signed the letter; party leaders charged that Cotton harmfully and inappropriately injected himself into foreign policy dealings with it.

“The reflex to simply counter the president no matter what has to be held in check because they are hurting their own cause,” said Rep. Adam Schiff (Calif.), the ranking Democrat on the House Intelligence Committee, speaking of the Republicans.

Cole said that he “probably would not have” signed the letter, but he didn’t disparage Cotton for writing it.

Former Senate Foreign Relations Committee chairman Richard G. Lugar (R-Ind.), who called the letter “an unfortunate venture,” suggested that Republicans may have signed on out of fear of getting tagged as too soft on Obama.

“It could be, given the general unhappiness Republican senators have had with the president, that most signed the letter to stay on board with others and not attract opposition from others who might have painted them as outliers,” said Lugar, who lost his bid for a seventh term to a Republican primary challenger in 2012.

In the Senate, Foreign Relations Committee Chairman Bob Corker (R-Tenn.) is trying to build support for a bill that would give Congress 60 days to review any deal that comes out of the negotiations with Iran. The bill has half a dozen Democratic sponsors and might win enough Democratic support to foil the administration’s plans.

White House Chief of Staff Denis McDonough sent Corker a letter Saturday charging that his bill goes “well beyond ensuring that Congress has a role to play in any deal with Iran.”

McDonough also said in the letter, which was first reported by the Huffington Post, that the president wants Congress to wait until a deal is reached before voting on legislation. He said a final deal could come by the end of June.

Robert Zoellick, former World Bank president and leading Republican foreign policy expert, said that “at some level, this conflict comes down to a case of [Obama’s] difficulties in preparing the way — and working with — Congress.”

Schiff, the California Democrat, said that the backlash against the Republican tactics on Iran could make GOP leaders more “circumspect” moving forward, but that he does not think “it will fundamentally change their eagerness to confront the president on Iran or any other foreign policy issue.”

At least on that point, Republicans and Democrats seem to agree.

“The tactics could change, but Republicans will likely continue to challenge Obama on foreign policy issues because most Americans agree that the White House has done a poor job of managing international crises that could impact our national security,” Republican strategist Ron Bonjean said in an e-mail.