Supporters of far-reaching immigration legislation see an uphill battle to get a bill to President Barack Obama's desk. They said outside advocates need to step up their efforts.
Republican Sen. John McCain of Arizona is a lead author of the comprehensive bill passed by the Senate last month. McCain warned that his side is not winning the fight.
He said there needs to be a concerted campaign that's so far been lacking, particularly from business and religious groups that can influence House Republicans.
Immigration legislation has been in limbo since the Senate acted on a bill last month.
House Speaker John Boehner said again Thursday that House will address the issue in a deliberate, step-by-step approach, starting with border security.
But no action is expected until September at the earliest.