The rallies, styled as “traveling salvation show tent revivals,” will be held in church parking lots and parks, with beer trucks, musicians and preachers in a bid to encourage evangelicals who have felt alienated from the Republican Party, Mr. Pagitt said.

The challenge is daunting. The initiative is small compared with the formidable ground operation of religious conservatives championing Mr. Trump’s nomination of Judge Brett M. Kavanaugh to the Supreme Court. Those field operations enjoy millions of dollars of financing in battleground states.

The budget for entire Vote Common Good tour is about $1 million. By comparison, each rally held when the evangelist Franklin Graham barnstormed California this spring to drum up the conservative evangelical vote cost nearly as much.

“The progressive left habitually rediscovers the strength of the evangelical vote and tries to counter it,” said Ralph Reed, the chairman of the conservative Faith and Freedom Coalition, which has field teams in 19 states and plans to knock on two million doors by Election Day.

“To be sure, imitation is the highest form of flattery,” he said. “But this effort will fall short because the religious left lacks the intensity, resources and infrastructure built over the years in the evangelical community.”

That isn’t stopping Democrats from trying.

“You are going to have a percentage of evangelicals who realize that the president’s behavior and policies are inconsistent with the teachings of Christ,” said Mr. Lieu, who is Catholic. “The Democratic Party is a very big tent party. You can have lots of different views. We are very accommodating.”