WASHINGTON — In a striking reach across party lines, the White House and key lawmakers agreed Thursday to reshape the nation’s immigration laws and give millions of illegal immigrants legal status. At the same time, borders would be tightened.

The compromise brought liberal Democrats and conservative Republicans together with top members of President Bush’s team on an issue that carries heavy potential risks and rewards for all involved.

The Senate will wade into an emotional and wide-ranging debate on the issue next week that promises to test the unlikely coalition that produced the deal. Almost instantly, the plan brought vehement criticism from both sides of the immigration issue, including liberals who called it unfair and unworkable and conservatives who branded it an overly permissive “amnesty.”

The proposal constitutes a far-reaching change in the immigration system that would admit future arrivals seeking to put down roots in the U.S. based on their skills, education levels and job experience, limiting the importance of family ties. A new class of guest workers would be allowed in temporarily, but only after borders were fortified and measures were in place to ensure the rules were followed.

Bush said the proposal would “help enforce our borders but equally importantly, it’ll treat people with respect.”

“This is a bill where people who live here in our country will be treated without amnesty but without animosity,” Bush said.

The formula was enough to satisfy liberal Sen. Edward M. Kennedy, D-Mass. — viewed as his party’s decisive voice on immigration — and Sen. Jon Kyl, R-Ariz., a conservative who has been adamantly opposed to past overhauls.

Kennedy hailed it as “the best possible chance we will have in years to secure our borders and bring millions of people out of the shadows and into the sunshine of America.”

Kyl said the measure wasn’t perfect, “but it represents the best opportunity that we have in a bipartisan way to do something about this problem.”

It was clear, however, that many Republicans and Democrats were deeply skeptical. Senate Majority Leader Harry Reid, D-Nev., called the proposal a “starting point” for next week’s debate and said it needed improvement.

“I have serious concerns about some aspects of this proposal, including the structure of the temporary worker program and undue limitations on family immigration,” Reid said.