Mr. Reid, Democrat of Nevada, said the Senate would vote Thursday on whether to limit debate, a process that requires 60 votes to succeed. He said he would pull the bill if he failed to get the necessary votes.

The majority leader said he wanted to complete work on the legislation this week, and he suggested that Republicans were trying to “stall this bill” with amendments. “When is enough enough?” he asked.

“People are looking for excuses on the Republican side to kill this bill,” he said.

His announcement provoked an outcry from Republican supporters and opponents of the bill, who said the Senate needed more time.

Senator Jon Kyl of Arizona, the chief Republican architect of the bill, said “it would be a big mistake” to try to invoke cloture this week.

A motion to cut off debate would be “an extreme act of bad faith,” Mr. Kyl said, and he asserted on Tuesday afternoon that “we are not anywhere near finishing this bill.”

The Senate Republican leader, Mitch McConnell of Kentucky, said, “The overwhelming majority of our conference would insist on having additional days to make sure that all of our important amendments have been given an opportunity to be considered.”

Even Senator Mel Martinez, Republican of Florida, a strong supporter of the bill, said, “I would not support cloture at this point because I don’t think that enough of our members have had an opportunity to have their amendments heard.”

Behind the scenes, senators were trying to work out agreements on what amendments to consider, so the legislation would not fail on a motion to limit debate.

Democrats have offered amendments to promote unification of families, by providing more green cards for relatives of American citizens and lawful permanent residents who want to come to the United States. For their part, Republicans have offered amendments to deny legal status to illegal immigrants who have defied deportation orders.

Mr. Reid said that if he could not muster the votes needed for cloture, he would move on to other matters — a vote of no confidence in the attorney general, Alberto R. Gonzales, and then energy legislation.

Mr. Reid said he saw only a tiny possibility that the Senate might return to immigration at a later date, but he added, “I never say never.”

If the immigration bill fizzles, it would disappoint some Democrats and Hispanic groups who see it as the best opportunity to gain legal status for many of the nation’s 12 million illegal immigrants.

Mr. Reid’s move could be a tactic to put pressure on the Senate to speed work on the measure by whittling down the number of amendments.

Senator Dianne Feinstein, Democrat of California, said she understood why Mr. Reid would want to do that. On the other hand, Mrs. Feinstein, a co-author of the bill, noted that it had not gone through any committee. “There is every reason why people would want to offer amendments,” she said.

By a vote of 71 to 22, the Senate on Tuesday adopted an amendment that seeks to protect American workers by requiring employers, in all cases, to try to recruit Americans before hiring foreign workers.

The Senate Democratic whip, Richard J. Durbin of Illinois, joined Senator Charles E. Grassley, Republican of Iowa, in offering this proposal. Theirs is one of the many unlikely alliances forged in the immigration debate.

“American workers should have the first chance to get every available job,” Mr. Grassley said.

By a vote of 62 to 31, the Senate rejected a proposal, by Senator Wayne Allard, Republican of Colorado, to alter the “merit-based system” that would be used to select future immigrants. Under this system, the government would evaluate would-be immigrants by awarding points for job skills and other attributes.

Mr. Allard wanted to eliminate a “supplementary schedule” of extra points that could be awarded to illegal immigrants who gain legal status and then apply for permanent-residence visas, or green cards.

He said the bonus points would give an “enormous advantage” to people who had entered the United States illegally.

Senator Edward M. Kennedy, Democrat of Massachusetts, said the extra points were a way to help agricultural workers. Without the extra points, he said, they would “lose out in any competition” with highly skilled, highly educated workers.