Sponsors of a comprehensive immigration overhaul that has stalled in the Senate today vowed to persevere in seeking passage of the legislation this summer.

“We are not giving up,” declared Sen. Edward M. Kennedy of Massachusetts, the chief Democratic sponsor of the measure (S 1348), which Majority Leader Harry Reid, D-Nev., pulled from the Senate floor Thursday night after three attempts to limit debate fell least 15 votes short of the 60 needed.

Arlen Specter, R-Pa., one of the Republicans backing the measure, predicted that GOP senators who united to block further action on the bill Thursday will eventually relent, after agreeing on a “finite list” of about 10 or 11 additional amendments they want to offer.

Jon Kyl, R-Ariz., said the work on an amendment list “illustrates that we have already begun the process of figuring out how to get this back together and concluded within the next few weeks.”

Kyl and Specter both chided Reid for moving to cut off debate before the Senate had debated even as many amendments as it considered last year on a similar immigration package. But they expressed optimism that the bill can be revived and passed.