"Here's the fact: We're not winning, so we've got to wage a campaign," the Arizona Republican told reporters.
"That doesn't mean a negative campaign. It means a positive campaign," he said.
"There are many members of the House that don't want to take up any bill at all, as you know," McCain said. "What our job is, we want to convince them to at least pass legislation, so that we can go to conference and work together."
McCain -- a member of the bipartisan "Gang of Eight" who wrote and negotiated an immigration-reform bill that passed the Senate 68-32 June 27 -- said supporters, including business, religious, labor and other groups, would use the August congressional recess to campaign in some 100 battleground districts for comprehensive immigration reform.
Spiritual leaders, police officers and business owners are expected to make the conservative case for immigration reform at town hall meetings, reported Politico, which interviewed McCain separately.
There will also be protests aimed at Republican leaders, Politico said.
All aspects of the campaign will seek to convince House Republicans they have no option but to pass broad immigration legislation.
House Speaker John Boehner, R-Ohio, has said the House will not consider the Senate bill, which he has called "flawed legislation rushed through the Senate."
House Republicans have united around a piecemeal approach.
"House committees will continue their work on a step-by-step, common-sense approach to fixing what has long been a broken system," Boehner said.
More than 90 Catholic college presidents sent letters to all Catholic House members, including Boehner, Wednesday urging them to support a comprehensive immigration bill.
"We hope that as you face intense political pressure from powerful interest groups, you will draw wisdom and moral courage from our shared faith tradition," said the letter, also signed by 60 prominent theologians and two former U.S. ambassadors to the Vatican.
"Catholic teaching values the human dignity and worth of all immigrants, regardless of legal status," they wrote. "We remind you that no human being made in the image of God is illegal."