Top Senate Republicans say if their party wins the majority November, they’ll support an immigration reform bill. Converts would likely include at least two GOP senators that voted against the measure that passed the Senate last summer.

Will a Senate GOP Majority Support Amnesty?

Immigrants suspected of being in the country illegally are escorted to a transportation bus after U.S. Border Patrol agents detained about 75 immigrants who’d been living in hut for several days in a brushy area Thursday April 17, 2014 near North 10 St. and Sprague St. in McAllen, Texas. (AP Photo/The Monitor, Gabe Hernandez)

“It could pass if we break it down into smaller pieces,” Senate Minority Whip John Cornyn (R-Texas), who could be majority whip if the bill passes, told The Hill. “[The House] has always been amenable to passing smaller bills on a step-by-step basis.”

Sen. Charles Grassley (R-Iowa) would be the chairman of the Senate Judiciary Committee if Republicans win control of the Senate in November, and told The Hill he would vote to pass a GOP version of the bill.

“We’d start over again next year,” Grassley said, when asked about the next steps if Congress does not pass immigration reform by September.

Some Republicans said they might have voted for the package if it were a series of bills, separating border enforcement measures from a pathway to citizenship for the some 11 million illegal aliens in the country.

“I’d make a decision about whether you could get more done by separate bills or a comprehensive bill,” Grassley said, adding he would have supported the previous bill if it had tougher border enforcement.

Last year, 14 Republican senators joined Democrats to pass the comprehensives immigration reform bill in the Senate, which has stalled in the House.

House Speaker John Boehner (R-Ohio) has given mixed signals about whether he would support bringing the Senate bill to the floor for a vote. President Barack Obama and other Democrats insist there are enough votes in the House to pass the measure even if a majority of the Republican caucus doesn’t support it.

Republicans are being pulled from two ends. The more conservative base and Tea Party voters oppose granting legal status to illegal aliens, which they call amnesty. However, earlier this week Thomas Donohue, president of the Chamber of Commerce made what sounded like a threat if Republicans don’t pass an immigration bill.

“If the Republicans don’t do it, they shouldn’t bother to run a candidate in 2016,” Donohue said. Then adding that it was a joke, he said, “Think about that. Think about who the voters are. I just did that to get everybody’s attention.”

However, Sen. Jeff Sessions (R-Ala.), the ranking member of the Senate Budget Committee, has objections.

“Washington can’t rewrite the law of supply and demand: we can’t rebuild our middle class if we continue to bring in record numbers of new workers for companies to hire at the lowest available wage,” Sessions said.

However, Sen. Marco Rubio (R-Fla.), one of four Republicans to make up the bipartisan “Gang of Eight” with four Democrats that sponsored the bill, said he is hopeful about 2015, The Hill reported.

“I certainly think we can make progress on immigration particularly on topics like modernizing our legal immigration system, improving our mechanisms for enforcing the law and I think if you did those things you could actually make some progress on addressing those who are illegally,” Rubio said.