Backers of a complex and contentious immigration overhaul resorted to a rare parliamentary procedure today to speed disposition of amendments that threaten to derail the bill.

Majority Leader Harry Reid, D-Nev., introduced a 373-page “clay pigeon” amendment that encompassed 27 separate amendments as a means of moving the chamber toward a final vote on the bill (S 1639) before the Fourth of July recess begins this weekend.

Reid is breaking the omnibus amendment into 27 individual parts, with votes on each either before or after tomorrow’s scheduled cloture vote to limit debate on the bill itself. That showdown will require 60 votes.

The individual amendments can be adopted only at the end of debate on the bill, unless they are agreed to by unanimous consent. In the meantime, the Senate began voting today on motions to table — and thus kill — specific amendments. Once tabled, an amendment is dead.

First up was a bid by Kay Bailey Hutchison, R-Texas, to require all adult illegal immigrants who want to stay in the United States on a probationary basis to return to their home country within two years in order to receive a Z visa allowing them to stay and work indefinitely. Her amendment was tabled, 53-45.

Senators also tabled, by 79-18, a Jim Webb, D-Va., amendment to limit Z visas to illegal immigrants who have been in the country at least four years and can demonstrate ties to their communities.