Key Republican and Democratic senators, working to attract more support for President Bush's stalled immigration bill, huddled Wednesday with Homeland Security Secretary Michael Chertoff to discuss tougher border security and workplace enforcement.

At a Capitol Hill meeting, the bipartisan group continued talks aimed at cobbling together enough backing from skeptical Republicans to quickly revive the measure that would grant legal status to as many as 12 million unlawful immigrants.

A day after Bush fielded criticism from Republicans whose opposition derailed the bill last week, the White House said it would be open to changes to the delicate bipartisan deal. Architects have argued their so-called "grand compromise" could collapse under the weight of "killer" amendments.

"You may have a carefully crafted compromise, but on the other hand, you have members of both parties who want to have their say and have their input," White House press secretary Tony Snow said. "Clearly, there will be some attempts to put together amendments that will be 'killer amendments,' but so far none have passed."

Snow also signaled support for the idea of pumping additional money into border security - an idea he said was "worth pursuing."

He played down the bitter divisions among Republicans on the issue. "This is not an internal 'fight,"' Snow said. Bush "considers fellow Republicans friends and colleagues."

Republicans are considering adding money to the bill for border security and workplace enforcement. Georgia Republican Sens. Saxby Chambliss and Johnny Isakson want a separate emergency funding bill that could total as much as $15 billion to pay for such measures.

Negotiators also were considering harsher penalties for immigrants who overstay their visas or re-enter the country illegally, according to Sen. Lindsey Graham, R-S.C.

"If you had mandatory jail time" for such offenses, Graham said, "I think it would create a deterrent."

Another possible amendment, he said, would prohibit employers from participating in a new temporary worker program if they repeatedly break the law by hiring illegal workers.

An amendment by Sen. Kay Bailey Hutchison, R-Texas, would require all illegal immigrant household heads to return to their countries of origin before obtaining legal status. Under the legislation, only those seeking green cards — permanent legal residency — would be required to return home first.

With senators maneuvering behind the scenes to try to craft a comprise package than can win passage, it is not clear when the measure will come up again for formal Senate floor debate.

Bush made a rare visit to the Capitol Tuesday to resurrect the bill, one of his top domestic priorities. It stalled in the Senate last week in the face of broad Republican opposition.

Republicans told the president at a closed-door luncheon that the American public has little faith that the government can secure the nation's borders or weed out illegal workers at job sites.

To alleviate such concerns, Bush said he was receptive to an emergency spending bill

"It's a highly emotional issue," the president said after attending a weekly Senate Republican luncheon.

"I don't think he changed any minds," conceded Sen. Mel Martinez, R-Fla., a supporter of the legislation.

But Martinez added that the president's appearance had helped nudge "people on the fence" to be more favorably inclined.

Bush administration officials also weighed in, with Chertoff telling skeptical conservatives in a letter that more manpower and money would be committed to improving border security and enforcement.

"Failure to act on this legislation will deny the country the safety and security provided by these enhanced enforcement measures," Chertoff wrote Tuesday night.

Many conservative Republicans have criticized the measure as an amnesty for millions of lawbreakers. Additionally, job approval ratings in the 30 percent range make it difficult for the president to bend even Republican lawmakers to his will.

Senate Majority Leader Harry Reid, D-Nev., said it was up to Bush and the Republicans to produce enough votes to revive the measure.

"We'll move on to immigration when they have their own act together," Reid told reporters.