WASHINGTON (AP) — Prospects for comprehensive immigration legislation this year grew murkier on the eve of an all-out push by a coalition of business, religious and law enforcement to persuade the House to overhaul the decades-old system.

At the same time, proponents seized on a California GOP lawmaker’s willingness to back a House Democratic plan as a Senate-passed measure remained stalled in the House.

But in a blow to their effort, Sen. Marco Rubio signaled support for the piecemeal approach in the House despite his months of work and vote for the comprehensive Senate bill that would provide a path to citizenship for the 11 million immigrants living here illegally and tighten border security.

The Florida Republican — son of Cuban immigrants and a potential presidential candidate in 2016 — had provided crucial support for the bipartisan Senate bill.

“Sen. Rubio has always preferred solving immigration reform with piecemeal legislation. The Senate opted to pursue a comprehensive bill, and he joined that effort because he wanted to influence the policy that passed the Senate,” Rubio’s spokesman, Alex Conant, said Monday in explaining Rubio’s backing for limited measures.

Since 68 Democrats and Republicans joined together to pass the Senate bill in June, opponents and many conservatives have stepped up their pressure against any immigration legislation, based not only on their principle opposition but their unwillingness to deliver on Obama’s top second-term domestic agenda issue.

The recent budget fight only inflamed conservative GOP feelings toward Obama.

Obama on Monday reiterated his call for Congress to complete action on an immigration overhaul before the end of the year. He said that represented the only way to end the record deportations of immigrants undertaken by his administration, actions he has tried to curtail by allowing young people who immigrated illegally into the United States — so-called Dreamers — to remain in the country under certain conditions.

“That’s why my top priority has been let’s make sure that we comprehensively reform the whole system so that we’re not just dealing with Dreamers, we’re also dealing with anybody who’s here and is undocumented,” he said in an interview with Fusion, a cable channel that is a collaboration of ABC News and Univision.

Most House Republicans reject a comprehensive approach and many question offering citizenship to people who broke U.S. immigration laws to be in this country. The House Judiciary Committee has moved forward with individual, single-issue immigration bills.

Although House Republican leaders say they want to solve the issue, which has become a political drag for the GOP, many rank-and-file House Republicans have shown little inclination to deal with it. With just a few legislative weeks left in the House, it’s unclear whether lawmakers will vote on any measure before the year is out.

Among the exceptions are Republican Reps. Mario Diaz-Balart of Florida and Darrell Issa of California, who have been working on possible legislation.

Diaz-Balart has said his bill would help those immigrants here illegally to “get right with the law,” purposely avoiding the word legalization that he said is interpreted differently in the fierce debate over immigration. Diaz-Balart had been slated to meet with the president on Tuesday, but the meeting was canceled and could be rescheduled, the lawmaker’s office said late Monday.

The congressman mentioned the session in an interview with Florida radio station WGCU and his office confirmed the meeting.

Determined to rally support, outside groups such as the U.S. Chamber of Commerce and Bibles, Badges & Business for Immigration Reform are descending on the Capitol Tuesday to lobby lawmakers to vote this year on immigration legislation.

Among those arriving in Washington on Monday was David Gaither, a former Republican state senator from Minnesota who served as chief of staff to former Gov. Tim Pawlenty. Gaither planned to meet with members of the Minnesota congressional delegation on Tuesday and deliver a simple message on immigration: Just fix it.

He said Monday that they will push for a comprehensive bill but were willing to accept piecemeal changes. The bottom line to lawmakers was “put service over self,” Gaither said.

Randy Johnson, senior vice president of the Chamber, told reporters on a conference call Monday that the effort is “about moving votes on the Hill in the right direction.”

Johnson said he was hopeful that the House could pass one or two of the single-issue bills before the end of the year, and left open the possibility of action early next year — an election year.

“I don’t think it’s the end of world if we can’t get it done by early February,” Johnson said. He said if it drags on until April or May, the prospects are dim.

Separately, Rep. Jeff Denham of California became the first Republican to back the House Democratic bill. Denham represents a swing district in northern California northeast of San Jose. He won his seat in 2012 with 53 percent of the vote.

“I want to fix it, I want to fix it once for my generation, for my children’s generation and a pathway to earned citizenship must be included in immigration reform legislation,” Denham said on a conference call with reporters.

The Senate bill, strongly backed by the White House, includes billions for border security, a reworked legal immigration system to allow tens of thousands of high- and low-skilled workers into the country, and a 13-year path to citizenship for the 11 million immigrants already here illegally.

The bill from House Democrats jettisoned the border security provision and replaced it with the House Homeland panel’s version. That bill, backed by conservative Republicans and liberal Democrats, would require the secretary of Homeland Security to develop a strategy to gain operational control of the border within five years and a plan to implement the strategy. It calls on the Government Accountability Office to oversee the steps being taken.

Denham said House Democrats were willing to incorporate his separate bill that would allow immigrants who are in the county illegally to become legal permanent residents if they enlist in the military and become a citizen after four years of service with an honorable discharge.

• Politics & Government
• Government
• Marco Rubio
• immigration reform