The Senate voted 67-27 Monday to advance a border security amendment to bipartisan immigration legislation, building momentum for a final vote later this week.

Fifteen of the “yes” votes were Republicans, suggesting supporters could hit the 70-vote threshold they hope to reach in the final vote. It is thought a big, bipartisan vote could put pressure in the GOP-held House, where immigration reform faces dimmer prospects.

The Republicans who voted “yes” were Sens. John McCain (Ariz.), Lindsey Graham (S.C.), Marco Rubio (Fla.), Jeff Flake (Ariz.) — the four authors of the legislation — and Sens. Bob Corker (Tenn.), Lamar Alexander (Tenn.), Kelly Ayotte (N.H.), Jeff Chiesa (N.J.), Susan Collins (Maine), Orrin Hatch (Utah), Dean Heller (Nev.), Mark Kirk (Ill.), John Hoeven (N.D.), Lisa Murkowski (Alaska) and Roger Wicker (Miss.).

Two Democrats, Sens. Mark Udall (Colo.) and Sherrod Brown (Ohio), missed the vote. If they’d been present, supporters would have won 69 votes on Monday.