Roger J. Stone Jr., a longtime adviser to Mr. Trump, said he expected the presumptive Republican nominee to grow aggressive on the banks. “Who’s been tougher on bankers than Donald Trump?” asked Mr. Stone, suggesting Mr. Trump could appeal to some of Mr. Sanders’s supporters. “He’s taken them to the cleaners. I think he has a healthy skepticism and deep knowledge of bankers and how they operate. He’s going to be tough on Wall Street.” Mr. Trump has said that “the hedge fund guys are getting away with murder.”

Mr. Stone added that Mr. Trump would also have a built-in layer of defense as he appeals to blue-collar voters, because he will be less vulnerable to traditional Democratic attacks over Republican efforts to rein in entitlement programs. “Unlike all these establishment Republicans, he’s been adamant about never touching entitlements,” Mr. Stone said. “You can’t run that play on Donald Trump.”

If by abandoning the traditional Republican playbook Mr. Trump were to put Michigan, Pennsylvania and Wisconsin in the Republican column, as some of his aides suggested, he would swing 46 electoral votes from states that have voted for Democratic presidential candidates since the 1980s.

“We lost two elections trying to do this by the traditional electoral map,” said Senator Richard M. Burr of North Carolina, one of the Republican senators who has embraced Mr. Trump.

But for every voter Mr. Trump wins over with his ad hoc populism, he risks repelling others — including conservatives who are aghast at how, on some issues, he is trying to outflank Mrs. Clinton on the left. While he may put parts of the Midwest back into play, at least initially, his approach could also endanger his prospects in some states that usually lean Republican.

“I think he’s more likely to take Michigan than he is to take Arizona,” said Mr. Flake, whose state is home to a fast-growing Latino population.

The unease on the right with Mr. Trump’s ideological positioning spans the party’s factions, alarming national security hawks, fiscal conservatives focused chiefly on promoting free markets, and the Christian right.