Thankful for a breakthrough, President George W. Bush on Saturday praised senators of both parties for delivering a potential deal to overhaul U.S. immigration policy.

The compromise aims to grant legal status to millions of people in the country unlawfully, stiffen border security and create a program for temporary workers. It also would reshape requirements for new immigrants and take measures to prevent illegal workers from getting jobs.

"I realize that many hold strong convictions on this issue, and reaching an agreement was not easy," Bush said in his weekly radio address.

"I appreciate the effort of senators who came together to craft this important legislation," he said. "This bill brings us closer to an immigration system that enforces our laws and upholds the great American tradition of welcoming those who share our values and our love of freedom."

A victory for Bush is far from assured. The proposal must get through the Senate, where debate begins Monday, and the prospects of such a plan are also uncertain in the House.

An unlikely alliance of liberal and conservative lawmakers championed the proposal, which was announced Thursday after months of private talks among senators and the White House.

The president used his radio address to tout the deal and build momentum for it, without expressly lobbying lawmakers to vote for it. For Bush, approval of a comprehensive plan to improve immigration — a thorny, complex matter — would be a signature second-term achievement.

The package faces opposition from both sides. Conservatives say it is too lenient on those who have broken the law; liberals warn it would be unworkable and unfair to migrant families.

Yet Bush said the deal has "all the elements required for comprehensive immigration reform."

The proposal orders that border improvements and a worker identification program must come first, as a trigger to other changes.

Among the key points, illegal immigrants could come forward and seek a "Z visa" and — after paying fees and a fine — ultimately get on track for permanent residency. That could take several years. Heads of households would have to return to their home countries first.

Guest workers would have to return to their home country after periods of two years. They could renew their visas twice, but would be required to leave for a year in between each time.

The deal also proposes a fundamental reordering of immigration priorities, moving the system from one based on family to one primarily designed to meet the needs of U.S. employers.

Bush said the deal would end "chain migration" by limiting the relatives who can automatically receive green cards to spouses and minor children.

The point, he said, is to build a system for "immigrants who have the skills, education and English proficiency that will help America compete in a global economy."

Bush spoke from his ranch, where he and first lady Laura Bush are spending the weekend.