WASHINGTON — President Bush pressed divided Republicans on Tuesday to support him on immigration overhaul, saying “status quo is unacceptable.”

The president, in a rare visit to the Capitol, told reporters after a luncheon with the Senate GOP membership that he recognized that immigration was an emotional issue and that many do not agree with him. Still, he said, “Now is the time to get it done.”

Bush mounted a personal effort to salvage his derailed immigration bill, as key lawmakers reached for a deal that could quickly revive the measure. He needs to change enough minds among GOP senators to push through a top domestic priority.

The measure, which legalizes up to 12 million unlawful immigrants and tightens border security, stalled last week in the face of broad Republican opposition.

Bush promised to work with senators in coming up with a measure he could sign. “The White House will stay engaged,” he pledged.

“Some members in there believe we need to move a comprehensive bill, some don’t,” Bush said. “I understand that. It’s a highly emotional issue.”

He said he hoped Senate Majority Leader Harry Reid, who supports the bipartisan legislation backed by the White House, “has the same sense of desire to move the product, the bill, that I do.”

“It’s going to take a lot of hard work, a lot of effort. We’ve got to convince the American people this bill is the best way to enforce our border. I believe that without the bill, it’s going to be harder to enforce the border. The status quo is not acceptable,” Bush said.

Bush has predicted he will prevail in his effort to win approval of an immigration bill. But his brief comments on Tuesday were muted, and he voiced recognition of the difficult work ahead.

Speaking with reporters after the president left, Senate Minority Leader Mitch McConnell, R-Ky., said the meeting with Bush was “wide ranging” and touched on other issues besides immigration, including Bush’s recent trip to Europe.

Sen. Trent Lott, R-Miss., called it “democracy working at its best” and said that Bush had signaled he “won’t sign a bad bill.”

“But he thinks this is an issue that needs to be addressed” and is “willing to work with us to get this job done,” Lott said. “I hope that the majority leader will work with us to move it forward,” Lott added.

Reid, D-Nev., had pulled the measure from the Senate last week when two efforts to cut short debate failed. The Democratic leader said he will bring up the measure again only if Democrats can be assured of more Republican backing.

Still, it was unclear how much influence Bush has among Republicans on immigration, given that it has sparked a backlash among some of the party’s core supporters, who see it as amnesty for people who sneaked into the country.

McConnell, asked whether he thought Bush had won over any more GOP senators in his presentation, said, “I think a lot of that will depend upon what it looks like in the end. And none of us know that yet.”

“Look, we had a very, very good discussion, including some of our members who are not — shall I say? — keen on this measure, and others who are still taking a look at it and trying to decide how they’re going to vote,” the GOP leader said. “So it was a good give and take. We didn’t expect anybody to stand up and holler that they had an epiphany.”

The fragile package promises a path of legalization for millions of undocumented workers in the United States while tightening borders and offering employers more temporary workers. The bipartisan bill supported by the White House is cosponsored by Sens. John McCain, R-Ariz., and Edward M. Kennedy, D-Mass.