Hoeven and Corker were looking at packaging their amendment with others on enforcement issues by other Republican senators in hopes of building a bipartisan consensus for the bill.
"We have some people on our side of the aisle that just are not going to support the immigration bill, period," Corker said Tuesday. "But I think there are a number of people on our side of the aisle that, if we could just get it tailored a little bit with a few other amendments, might be willing to send it over to the House. And there are a lot of people who think it might come back over here in a little better form than it leaves."
The GOP-led House was confronting its own obstacles on immigration. Late Tuesday, the House Judiciary Committee agreed on a party-line 20-15 vote to approve a tough enforcement-focused immigration bill, over objections from Democrats and chants of "Shame, shame" from protesters. The measure would make being in the U.S. illegally a federal crime punishable by prison time, instead of a civil offense as it is now. It also would empower state and local law enforcement officials to enforce federal immigration laws.
On Wednesday, the committee was to take up a bill creating a temporary agriculture worker program.
The opposition among many House Republicans to sweeping action on immigration was on display Wednesday as Rep. Steve King, R-Iowa, an immigration hardliner, convened a six-hour press conference outside the Capitol to highlight opposition to the Senate bill. People in the crowd held signs opposing "illegal aliens" and criticizing Sen. Marco Rubio, R-Fla., a conservative author of the Senate bill, as "Obama's Idiot."
Opposition in his conference to any immigration bill with a path to citizenship put House Speaker John Boehner, R-Ohio, into a difficult position. On Wednesday, a day after trying to reassure House Republicans that he wouldn't bring immigration legislation to the floor without majority support from Republicans, Boehner was to meet with the Congressional Hispanic Caucus, which includes many liberal Democrats who are eager to see the House act on far-reaching legislation.
In the Senate, the bipartisan bill that President Barack Obama supports appeared on track for a final vote as early as July 4.
The CBO said in its report and accompanying economic analysis that the Senate legislation would raise economic activity in each of the next two decades, in part because of the legal immigration fostered by the measure and also because millions of workers currently in the country illegally would join the legal workforce and pay taxes.
The CBO said the bill would increase gross domestic product by 3.3 percent over the next 10 years compared with current law and by 5.4 percent over the following decade.
CBO also said that the immigration bill would decrease federal red ink by $197 billion over a decade and $700 billion in the following 10 years as increased taxes paid to the government offset the cost of benefits for newly legal residents. The legislation would cost about $2 billion annually to implement over the next 20 years.
CBO also said that average wages would decline through 2025 as a result of the bill and that unemployment would go up slightly.