About 250 immigration rights protesters gathered at the U.S. Immigrations and Customs Enforcement office with a goal of stopping future deportations on Monday in Phoenix, Ariz. (Ross D. Franklin/AP)

President Obama and his Democratic allies are using momentum from reopening government to renew their attempts to persuade House Republicans to support a comprehensive immigration reform bill by the end of the year.

“Let’s start the negotiations,” Obama said Thursday, speaking at the White House a day after Congress agreed on a plan to end the government shutdown and raise the debt limit. “But let’s not leave this problem to keep festering for another year or two years or three years.”

With Democrats convinced that they have the GOP on the defensive, the president cited the passage of an immigration bill, along with securing a long-term budget and a farm bill, as top priorities over the next three months. Senate Majority Leader Harry Reid (D-Nev.) and Sen. Charles E. Schumer (D-N.Y.) also place immigration atop the Democratic agenda for the remainder of the year.

But it’s not clear that GOP lawmakers, who took the brunt of public blame for the 16-day shutdown, will be forced to the negotiating table. Some key Republicans said this week that Obama’s hard-line position during the fiscal talks, in which he refused to negotiate, had further damaged his credibility with a caucus already skeptical of his agenda.

Rep. Raul R. Labrador (R-Idaho) told a conservative audience on Wednesday that “it would be crazy for the House Republican leadership to enter into negotiations with him on immigration.”

Labrador, who dropped out of a bipartisan House effort last spring to strike a comprehensive immigration deal, added: “Anything we negotiate right now with the president on immigration will be with that same goal in mind, which is to destroy the Republican Party.”

House GOP leaders remained largely silent on the issue Thursday. A spokesman for Speaker John A. Boehner (Ohio) said he “remains committed to a common-sense, step-by-step approach that ensures we get immigration reform done right.”

Boehner has said the House will not support a bipartisan plan approved by the Senate in June that features a 13-year path to citizenship for the nation’s 12 million undocumented immigrants. Instead, House leadership has said it is pursuing a series of smaller-scale bills, a tactic that immigration advocates view as a cloaked attempt to kill any momentum for a deal.

One key question is how the fiscal standoff and its aftermath might effect Boehner’s approach to immigration.

On one hand, immigration advocates said, Boehner has appeared to emerge with more respect from the conservative bloc of the GOP caucus long skeptical of his willingness to take on the White House. That could embolden him to push for a broader set of immigration proposals that could result in a conference with the Senate.

On the other hand, Boehner was forced to bring a short-term spending plan to the House floor late Wednesday that was approved with mostly Democratic support, a move the speaker acknowledged was a political loss for his party. That could make him fearful of pursuing a vote on an immigration plan that would also likely depend heavily on Democrats.

“Have the hard-liners been empowered or is the leadership getting tired of their reign?” said Tamar Jacoby, the chief executive of Immigration Works, which advocates for immigration reform on behalf of small businesses. “Does the leadership feel they have new room to maneuver or not? I don’t think anyone knows how that dynamic has been shaken up.”

Kevin Appleby, migration policy director for the U.S. Conference of Catholic Bishops, which favors immigration reform, said that Obama “needs to frame it in terms of getting something done for the American people and restoring faith in Washington. When you get a sense where the polls are after the budget, Republicans will want to stabilize themselves. I think there’s some momentum of the victory that the president can use as leverage.”