Updated

President Bush, trying to salvage an immigration overhaul legislation, endorsed a plan Thursday that would lock in money for border security as way to win over conservative lawmakers and a skeptical public.

"We're going to show the American people that the promises in this bill will be kept," Bush said in a speech to the Associated Builders and Contractors.

Bush got behind a proposal to set aside money collected through fees and penalties for tougher border security and workplace enforcement. Two Republican senators, John Kyl of Arizona and Lindsey Graham of South Carolina, have proposed such an amendment.

Bush said the measure would "show the American people that we're going to do our jobs of securing this border once and for all."

The provision would immediately divert $4.4 billion toward border security, with that amount to be paid back once new fees are in place. The point would be to ensure that border security would not be subject to the whims of the yearly budget negotiations.

The move is also part of a White House effort to cobble together a winning coalition, vote by vote. Some lawmakers are withholding support for the broad-based bill because of deep skepticism that border security will actually improve.

With many questions unanswered, it was unclear how much of a concession the move amounts to for Bush.

The White House did not have an estimate of how much money the provision would generate yearly toward border security. It also could not say whether the money would be in addition to currently planned border security funding levels or just a way to dedicate funds to that purpose. And it wasn't clear what budget account would be drawn down to pay for the initial $4.4 billion.

A bipartisan group of senators crafted a fragile compromise on the immigration bill that Bush supports. But the deal is in deep trouble, because many Republicans oppose that it provides a way for millions of immigrants who entered the country illegally to become legal.

The group behind the compromise was hoping to reach agreement to allow votes on a limited set of changes from the Republican and Democratic sides in exchange for a commitment from GOP holdouts to let debate on the bill resume. Architects have argued that their so-called "grand bargain" could collapse under the weight of too many amendments, or those designed as "poison pills."

Bush said the bill emphasizes security by requiring tougher border and workplace measures before new options for immigrants and guest workers could begin. Already, he said, border agents are capturing and sending home huge numbers of people trying to cross illegally.

"They're working hard down there, and they're making progress," Bush said. "People are doing the jobs we expect them do, and now we're going to build on that progress."

The legislation stalled last week when only seven GOP senators supported a Democratic bid to limit debate -- called a cloture vote -- and expedite a final vote.

White House press secretary Tony Snow said the White House feels good about its chances for bringing the bill back to the floor now.

"We feel confident there are going to be enough votes for cloture," he said.