Sen. John McCain (R-AZ) gave the clearest indication that proponents of comprehensive immigration reform may make their final–and strongest–push to get legislation passed next year after House Republicans make it through their primaries.

“I think conventional wisdom is that time is not on our side,” McCain told reporters on Monday after an event in Chicago. “But there are a number of members of Congress who have primaries and when those primaries are done, they may be more inclined to address the issue of comprehensive immigration reform.”