Republicans have grown accustomed to the president’s lack of discipline and inability to reliably carry a message. But operatives overseeing the midterm effort and some lawmakers facing difficult re-elections are growing more alarmed that Mr. Trump’s fixation on the Russia inquiry, personal slights and personality clashes inside and outside his White House are only encouraging his congressional and conservative news media allies to swerve off message.

The party has finally gotten some good signs. The president’s approval ratings have been inching up in recent polling, fewer voters are indicating a preference for a Democratic Congress and some polls show Mr. Trump starting to get more credit for the booming economy than former President Barack Obama.

But even as voters begin to see more take-home pay, companies add jobs and employees receive bonuses, their votes are not necessarily going to drift to the Republicans in November. Many Americans are still uncertain that they will benefit from the tax measure, Mr. Bliss conceded. He cited a wave of private polling and focus groups that his organization has conducted this year revealing much of the electorate to be skeptical that they would receive a tax cut from the bill, which was signed into law in December.

That is in part because of what mainstream Republicans describe as a destructive cycle of incentives: Mr. Trump reacts to Fox News segments about the Russia investigation or another controversy, encouraging more such coverage and prompting House conservatives from largely safe seats to make their own incendiary comments, which win them television invitations and attention from the president. Such notoriety might help those lawmakers in their deep red districts, but they do nothing for the party’s overall political standing.

“These guys are performing for the president when they go on TV,” said Jason Roe, a longtime Republican strategist who is consulting on a series of at-risk House districts in California.

Representative Matt Gaetz of Florida, a first-term Republican who is one of Mr. Trump’s most visible champions outside the White House staff, all but said as much.