The White House is intensifying its push to get an immigration overhaul through Congress this year, but House Speaker John Boehner cast new doubt Wednesday about the prospects for quick action.

President Barack Obama brainstormed at the White House Wednesday with religious leaders over how to persuade House Republicans to move on the issue. Last week, the president met with business executives to urge them to speak out for action. He is planning other immigration events on the road, with a mix of national and local outreach,...