The timing of when to grant legal status to the nation’s estimated 11 million illegal immigrants has emerged as the key point of dispute between the House and the Senate, which is poised to approve its immigration bill as soon as Thursday.

Differences over the issue could keep the House and Senate from reaching a deal and prevent President Obama from fulfilling the top priority of his second term despite the momentum gained from a successful Senate vote.

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Republicans in the House say the border security amendment added to the Senate bill Wednesday to bolster GOP support in both chambers improves the legislation — but not enough to gain their support.

Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) again assured House Republicans in a private meeting Wednesday that the House would not simply take up and pass the Senate bill, leaving prospects for immigration reform reaching Obama’s desk unclear.

Conservatives said the border security amendment does not address what they see as the Senate bill’s fatal flaw: It grants the nation’s illegal immigrants provisional legal status before border security and enforcement enhancements are implemented.

“I’m not going to call it a fig leaf. I think it is an actual enforcement amendment,” said Rep. Raúl Labrador (R-Idaho), a former immigration lawyer who worked for months with a bipartisan House group crafting immigration legislation. “The issue with it is that it legalizes 11 million people before it is put into place all the way.”

The likelihood of an eventual compromise could hinge, Republicans say, on whether Democrats give ground on the timing of legalization.

“There’s no question that’s a major dividing point,” said Rep. Tom Cole (R-Okla.).

Senate Democrats have held out hope that their concessions on border security will pave the way to a deal with the House.

And there have been some positive sides from key House Republicans.

Rep. Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.), a champion of comprehensive immigration reform, said on Tuesday that passage of the amendment brokered by GOP Sens. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.) and John Hoeven John Henry HoevenDavis: The Hall of Shame for GOP senators who remain silent on Donald Trump Bottom line Bipartisan senators seek funding for pork producers forced to euthanize livestock MORE (N.D.) moved the Senate “closer to the House’s position,” and made a final bill “more likely.”

Yet House leaders have repeatedly said the proposal will have to move further to the right to have any chance across the Capitol.

The Corker-Hoeven amendment “made the bill better, no question about that, and the mere fact that it won significant Republican support is an indication of that,” said Cole. “But is that sufficient to make it pass over here? No.”

The amendment provides $30 billion for border security and requires the construction of 700 miles of fencing on the U.S.-Mexico border before immigrants in a provisional legal status can apply for a green card on a path to citizenship that, for most, will take at least 13 years.

But most illegal immigrants could still obtain provisional legal status within six months of the law’s enactment, once the secretary of Homeland Security has submitted border security and fencing strategies to Congress.

“If you flip it, and you say the Corker-Hoeven amendment has to be in place before you legalize 11 million people, then I would be more supportive of it,” Labrador said.

At issue, Republicans say, is the lack of trust that their constituents have in the federal government to enforce immigration laws and secure the border after immigrants are legalized.

“My constituents believe that border security is a condition precedent,” said Rep. Trey Gowdy Harold (Trey) Watson GowdySunday shows preview: Election integrity dominates as Nov. 3 nears Tim Scott invokes Breonna Taylor, George Floyd in Trump convention speech Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-S.C.), chairman of the House Judiciary Committee’s subcommittee on Immigration. “I cannot go to my district and ask people to trust us. I just can’t.”

The Obama administration and Senate Democratic negotiators have balked at any delay in legalization, arguing the path to citizenship must be workable and clear from the start of the process. Democrats also see as unrealistic GOP demands for enhanced interior enforcement and for the employer e-verify system to first be implemented before legalization occurs.

House Republicans plan to meet on July 10 to discuss immigration, after which GOP leaders could bring to the floor a series of individual bills the Judiciary Committee is approving along party lines.

“We’ll do our own bill, through regular order, and it’ll be a bill that reflects the will of our majority and the people we represent,” Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE told Republicans behind closed doors on Wednesday, according to a person in the room.

Boehner has said he would not bring up an immigration bill that lacks the support of a majority of his conference, and two more House conservatives said Wednesday he could lose his job if he goes back on his word.

“Whether he should or not, I think he would,” said Rep. Matt Salmon Matthew (Matt) James SalmonCOVID-19's class divide creates new political risks Arizona voters like Kyl but few think he'll stick around Former Sen. Jon Kyl to replace McCain in Senate MORE (R-Ariz.), who is circulating a petition calling for the House to formalize the “Hastert Rule,” which refers to a policy of only taking up measures that have the support of “the majority of the majority.”

“The American people elected a Republican majority in the House of Representatives,” added Rep. Tom McClintock (R-Calif.). “For a leader of that majority to use his authority to circumvent that majority would be cause for removal in my judgment.”

Boehner would have more options if a bipartisan group of House lawmakers finishes its work on immigration, but negotiators are still haggling over details and have missed repeated self-imposed deadlines for introducing their bill. The members have kept their proposal almost entirely under wraps, and while Democrats in the group have begun briefing their colleagues, most rank-and-file Republicans remain in the dark about their work.

“What bipartisan group?” Rep. John Fleming John Calvin FlemingTrump wants Congress to delay Census deadlines amid pandemic Meadows sets up coronavirus hotline for members of Congress The Hill's Morning Report - Iran strikes US bases in Iraq; Trump to speak today MORE (R-La.) said when asked about it on Wednesday. “They’re an apparition.”