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The 2006 and 2007 efforts show just how elusive an immigration deal can be.

In 2006, the key bargain was to grant a path to citizenship only to illegal immigrants who had been in the country the longest. That bill passed the Senate but was never taken up by the House, which instead pushed through immigration enforcement measures.

The next year, President Bush, Mr. Kennedy and Mr. Kyl led a bipartisan group that reworked the entire immigration system, granting legalization to nearly all illegal immigrants and introducing a point system to determine how future legal immigrants would be selected. That bill was blocked on a bipartisan majority filibuster.

Mr. Kyl, who is now the No. 2 ranking Senate Republican, said the consensus that appeared to exist in 2007 is gone, and he said the big items he fought and won in that bill “are just not in the proposal” that Mr. Schumer and Mr. Graham released last month.

Several news reports said Mr. Schumer is hoping that Sen. John Cornyn, Texas Republican, would be willing to join forces. Mr. Cornyn is the ranking Republican on the immigration subcommittee on which Mr. Schumer serves as chairman.

Mr. Cornyn wrote his own immigration proposal along with Mr. Kyl several years ago but did not join the 2007 efforts. Mr. Cornyn, who as a Texan has a close view of border issues, is also chairman of Senate Republicans’ campaign committee, and signing on to an immigration bill could hurt his efforts there.

“I’m interested in trying to find a middle ground but I don’t think we’re anywhere near close,” Mr. Cornyn said. He also said he’s been asking to see exactly what Mr. Schumer and Mr. Graham have in mind but that they haven’t shown him anything.

“I don’t know if that exists,” he said.

Mr. Schumer said in a statement that he is still trying to get Republicans to help write the agreement, so there is no final bill to shop to senators such as Mr. Cornyn.

“We have a framework, but not a final bill yet, although we are close. So we are not approaching Republicans with a ‘take-it-or-leave-it’ mentality,” he said. “What we are really looking for is someone who’d like to flesh out the remaining details of our framework and really help us shape the bill so it can receive broad, bipartisan support.”

Texas’ other Republican senator, Kay Bailey Hutchison, is also not co-sponsoring the legislation, according to her senior legislative adviser.

It likely will be easier for Mr. Schumer to find a Democrat to co-sponsor his legislation. Sen. Mark Warner, Virginia Democrat, has been mentioned.