Washington (AFP) – With the budget crisis barely resolved, U.S. President Barack Obama is already urging Congress to complete a stalled immigration overhaul — and his Republican rivals don’t share his enthusiasm.

“We should finish the job of fixing our broken immigration system,” Obama said Thursday. “Let’s start the negotiations. But let’s not leave this problem to keep festering for another year, or two years, or three years. This can and should get done by the end of this year.”

An overhaul was in the works earlier this year.

In June, the Senate, dominated by Obama’s Democratic allies, passed a historic reform package that would create a pathway to legal status and eventual citizenship for millions of undocumented immigrants.

The Senate plan, crafted and approved with Republican support, would strengthen the border with Mexico and reorganize the visa system to give priority to high-demand fields, including engineers and farm workers.

But in the House of Representatives, Republicans hold the majority, and they are more hostile toward so-called “amnesty” for the millions of foreigners living illegally in the United States.

According to Democrats, immigration reform provides a chance to improve the image of conservatives, whose popularity sank after being blamed for the recent political paralysis in Washington.

“We have here a golden opportunity,” said Democratic political consultant Maria Cardona. “We have a window of opportunity of one or two months, when the House can vote the reform.”

Democratic Congressman Luis Gutierrez was more cautious.

“It is hard to be optimistic about the prospects for anything happening in a bipartisan manner on Capitol Hill these days,” he said, though predicting immigration reform could be taken up “before the end of the year.”

But other lawmakers argue that the budget crisis has in fact angered Republicans, who will be slow to grant Obama a new legislative victory.

“It’s not going to happen this year,” said Republican Representative Raul Labrador, a Tea Party favorite.

“After the way the president acted over the last two or three weeks where he would refuse to talk to the speaker of the House… they’re not going to get immigration reform. That’s done,” he told the USA Today newspaper.

Representative Aaron Schock agreed, telling reporters: “I’m not sure many on our side are getting prepared for immigration reform or any other domestic issue other than dealing with our debt.”

Some Republicans are in favor of immigration reform, which could help the party regain some influence among the increasingly critical contingent of Hispanic voters, who largely cast Democratic ballots today.

Both sides have backed border reinforcement, improving controls to prevent undocumented immigrants from getting hired, and increasing the number of visas for highly qualified workers. The House could pass related measures individually.

But offering citizenship to people who came to the United States illegally remains the most difficult point of contention, and Democrats are refusing to consider any reform lacking a pathway to bring illegal immigrants out of the shadows.

“I do think it is important that we be realistic about what the House can support and what they are working on,” said Republican Senator Marco Rubio, whose family is Cuban.

Despite some points of agreement between both sides, “there are other areas that are going to be more difficult to find consensus… now given the lack of trust in government and the way that this White House and the Democrats have behaved over the last three weeks,” he told Fox News.

“We cannot ignore that, that is going to be a factor moving forward in all this,” he said.