After a luncheon with the Senate GOP membership, the president said 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."
But even a personal plea from the president didn't influence one of the bill's harshest critics, reports CBS News correspondent Sharyl Attkisson.
"He didn't persuade me," said Sen. Jess Sessions, R-AL, "because my concerns go to my belief that the bill won't work effectively."
The bill, which would legalize up to 12 million unlawful immigrants and tighten border security, stalled last week in the face of broad Republican opposition.
Mr. Bush promised to work with senators to produce 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," Mr. Bush said. "I understand that. It's a highly emotional issue."
But it's not just the minds of senators that have to be changed, adds Attkisson.
In a recent national poll, the immigration bill got a mostly negative reaction from those who've heard of it. Forty-one percent are opposed and just a third favor it. Twenty-six percent have no opinion.
Mr. Bush 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," Mr. Bush said.
The president 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.
Republican Senate leader Mitch McConnell said he wasn't sure if the president changed any minds, reports CBS News correspondent Bob Fuss.
"I think a lot of that will depend upon what it looks like in the end. And none of us know that yet," said McConnell, R-Ky.
McConnell said the meeting with Mr. Bush was "wide ranging" and touched on other issues besides immigration, including Mr. Bush's recent trip to Europe.
Reid, a Democrat, 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 Mr. 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.
"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," McConnell 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, a Republican, and Edward M. Kennedy, a Democrat.