Updated

President Bush, promoting bipartisan immigration talks as they reach a critical stage, said Saturday that Republicans and Democrats are building consensus that could produce a bill this year.

"I am optimistic we can pass a comprehensive immigration bill and get this problem solved for the American people this year," Bush said in his weekly radio address.

Bush used the address to put pressure on senators as they prepare to hold a vote on the contentious issue next week. Signing an overhaul into law would be viewed as a marquee domestic achievement for the president.

He has dispatched two members of his Cabinet, Homeland Security Secretary Michael Chertoff and Commerce Secretary Carlos Gutierrez, to Capitol Hill for almost daily closed-door meetings with a handful of Republicans and Democrats to cut an immigration deal. The group is eyeing a Tuesday deadline for a compromise.

"These meetings have been productive. We've been addressing our differences in good faith, and we're building consensus. Both Republicans and Democrats understand that successful immigration reform must be bipartisan," Bush said.

Sen. Edward M. Kennedy, D-Mass., thanked Bush for "addressing the nation on this critical issue and emphasizing the common goals that we share.

"The American people will be watching and waiting to see if the Senate can come together on immigration reform and strike the right balance between strengthening our security and our economy and enacting laws that uphold the humanity and dignity of those who come here seeking a better life," Kennedy said.

Both sides have an interest in addressing the topic, which polls show is among Americans' top concerns. It's also a top issue for Hispanic voters, a fast-growing segment of the electorate that is being hotly contested by the two parties.

"The politics are pointing to action. What's difficult is that squaring the circle on the policy differences between the two parties is hard," said Frank Sharry, the executive director of the National Immigration Forum.

"Politically it makes sense for the key players to get it done this year, and before the next election season kicks in," Sharry said.

Still, the negotiations have proceeded in fits and starts, with key players agreeing on broad principles but not always specifics, and both parties' core constituencies becoming increasingly nervous that their leaders will compromise too much on an emotional and highly complicated issue.

Talks were to continue throughout the weekend on a possible deal that would first secure the U.S.-Mexico border and implement an elaborate high-tech identification system for immigrant workers, and only then give an estimated 12 million illegal immigrants living in the U.S. a chance at legal status — after paying high fines, returning home and waiting as long as 13 more years.

The proposal would also create a guest worker program for new arrivals, but it would prevent many of them from staying in the U.S. The ability of immigrants to bring their families into the country would be limited.

Senate Majority Leader Harry Reid, D-Nev., has set a vote for next week to bring up an alternative plan that passed the Senate last year with wide support from his party but substantial GOP opposition. Republicans have said they would block the move, arguing that the bipartisan talks should be given time to bear fruit.

Without a deal by Tuesday, the stage would be set for a partisan clash over immigration when the vote occurs, expected on Wednesday.

Bush has long called for an immigration overhaul that would create a guest-worker program and allow illegal immigrants a chance at citizenship, as well as bolstering border security. He supported the 2006 measure, which died in the House amid opposition from his own party's conservatives.

The potential compromise being discussed now is an effort to meld key elements of that plan, including allowing illegal immigrants to stay in the U.S. legally, with tougher provisions that could draw GOP support.