WASHINGTON — The Bush administration and key senators are working on a deal that would delay a sweeping immigration overhaul until the border is fortified and leave illegal immigrants waiting up to 13 more years to gain legal status.

Officials familiar with the discussions say that despite a series of concessions by Republicans and Democrats, a final agreement may not come before the Senate opens debate on the issue next week.

Still, the outlines of a possible deal have taken shape in almost daily secret talks involving two members of President Bush’s Cabinet. As contemplated, the proposal would delay the process of giving legal status to undocumented immigrants and guest worker visas to new arrivals until the administration beefs up border security and implements a high-tech identification system for temporary workers. Such measures are expected to take up to two years.

Even then, officials said it would take up to 13 years — along with large fines and a trip to their home country — before the 12 million men, women, and children estimated to be in the U.S. illegally could get permanent legal status, or green cards. The government would spend eight years clearing visa backlogs for immigrants currently waiting in line, and then spend about five years processing those here illegally.

Senator Kennedy, a Democrat of Massachusetts, has been leading negotiations with Republican senators and White House officials in hopes of cutting a deal on the issue before the Senate wades into an explosive immigration debate.

Absent such a compromise, Senator Reid, the majority leader and a Democrat of Nevada, is expected today to bring up a much more liberal measure approved last year, in preparation for a lengthy and wide-ranging debate on the matter starting next week.

Senator Specter, a Republican of Pennsylvania, one of the negotiators, made a plea yesterday for more time to reach a bipartisan deal, warning that rushing a debate could provoke a filibuster. Mr. Specter called the emerging agreement a “grand bargain.”

The political stakes for both parties are high. Democrats are eager to deliver a measure that appeals to their liberal base by allowing the huge undocumented population to earn legal status and welcoming new immigrants.

Republicans are seeking to neutralize an issue that party strategists believe hurt them in the 2006 elections. Some GOP lawmakers, however, are wary of alienating core conservative backers who want to crack down on immigration and enact stricter laws.

A group of House Republicans led by Rep. Lamar Smith of Texas, the senior Judiciary Committee member in his party, wrote to senators yesterday decrying as “mass amnesty” any bill that grants legal status to undocumented immigrants instead of deporting them.

Reshaping the immigration system is a top priority for President Bush, who has said he hopes Congress can deliver a measure by the end of summer.

Weeks of negotiations have yielded tentative agreements within the bipartisan group on many divisive issues, but they have yet to agree to any package, and both sides face major risks.

Mr. Kennedy must balance his appetite for a deal against the concerns of liberal groups that find the conditions for immigration policy changes — sometimes referred to as “triggers” — punitive and unacceptable. They also object strenuously to proposed changes that would curtail legalized immigrants’ ability to petition for relatives to come to the United States and would forbid temporary workers from bringing family if their income is below 150% of poverty level and they don’t have health insurance. Republicans, led by Senator Kyl, a Republican of Arizona, are fearful of appearing to embrace an overly permissive measure.

“You just can’t comprehensively reform something until you first solve the problem, and the problem is an insecure border. Once it’s secure, then you can make your reform work,” said Senator Isakson, a Republican of Georgia, a leading proponent of the conditions.

The steeper obstacles for an immigration program come as the White House works to gain more Republican backing for an overhaul. The measure up for discussion in the bipartisan talks is tougher than one that the Senate passed a year ago with broad Democratic support but relatively few GOP votes.

“They’re not deal-breakers for us, but the flexibility has to be good enough that I can go to our community and say, within the context of the policy, this is worthy enough of supporting — but not a deal at any cost,” said Senator Menendez, a Democrat of New Jersey, who has been in on the talks.

In Miami’s Little Havana yesterday, the Coalition for Comprehensive Immigration Reform launched a press campaign targeting Senator Martinez, a Republican of Florida, the party chairman who supported last year’s measure, for backing the Bush administration’s new, more restrictive stance.