The Senate, with Bush's backing, passed a bill last year that did both, but it wilted into campaign fodder for November's midterm elections after House Republicans staged hearings around the country opposing it.
"Without the administration's earnest engagement on this issue, our efforts are likely to suffer the same fate they did last year," Senate Judiciary Chairman Patrick Leahy said at a hearing he called to weigh the administration's support.
Homeland Security Secretary Michael Chertoff and Commerce Secretary Carlos Gutierrez told the committee that Bush is committed to seeing a sweeping immigration bill become law, though they were careful not to wade too much into details.
"Secretary Chertoff and I come before you today on behalf of the president with a simple message: We believe that with some hard work a solution can be found, and we pledge to roll up our sleeves and work with you on a bipartisan basis," Gutierrez said.
Supporters of allowing some of the estimated 11 million to 12 million illegal immigrants to remain in the United States are expected to unveil an immigration bill as early as next week.
Closed-door meetings to draft the legislation have been going on for months with Sens. Edward M. Kennedy, D-Mass., and John McCain, R-Ariz., and Reps. Luis Gutierrez , D-Ill., and Jeff Flake, R-Ariz.
"There aren't many issues where President Bush and this Congress are going to be able to come together. ... It's an opportunity that none of us can afford to squander," Flake said.
Bush has raised the immigration issue several times this year. He named it the issue on which he would find most agreement with Democrats after they won control of Congress last November.
A sticking point is whether to allow immigrants who come as guest workers in the future to remain in the country and seek legal residency after a prescribed period of work.
Many conservatives and immigration-control groups think they should have to return home. Some Democrats also have trouble with bringing in additional immigrants to work because of labor union concerns that they will take jobs away from Americans.
"What interests should be served, the interests of poor people or those around the world ... or shouldn't it be the interests of the people of the United States?" said Sen. Jeff Sessions, R-Ala.
Kennedy said the U.S. already grants employers of high-skilled immigrants a chance to seek legal residency for the worker.
Last year's Senate bill divided illegal immigrants into three groups based on how long they had been in the country and set up different criteria for each. Those in the country less than two years had to leave.
"Whatever measures are passed must work in the real world," Chertoff said.