Some Democrats have actually weaponized the tax package against their opponents, including Danny O’Connor, a Democrat running in a tight race against a Republican incumbent, Troy Balderson, in Ohio. In the run-up to a special election in August — they are squaring off again in Tuesday’s general election — Mr. O’Connor and his backers spent more money attacking the tax cuts than Mr. Balderson and his allies spent defending it.

Traditional Republican pollsters and strategists said hewing too closely to Mr. Trump’s incendiary strategy could contain more risk than reward for candidates in the campaign’s final days. They warn of possible backlash among minority voters and college-educated whites, two groups that could be especially crucial in deciding congressional control.

Polling suggests that the same suburban independents who broke for Mr. Trump in the final days of the 2016 election could shift back to Democrats this time around. And Republican campaign veterans said that while Mr. Trump’s fear-mongering is firing up his base, it could energize other voters who were previously apathetic to vote for a Democrat next Tuesday.

“The problem is Republicans have a good story to tell in the economy,” said Mike Murphy, a former adviser to Jeb Bush, John McCain and Mitt Romney. “But the Republican with the largest microphone only wants to go on these rants about immigration.”

Mr. Trump, he said, is “managing to offend every swing voter in the country.”

That could prove particularly risky in competitive races for the House of Representatives. Republicans are defending many seats in diverse metropolitan regions where the president’s heated language could prove a hindrance.

Mr. Trump even acknowledged at his rally Friday that Republicans could lose the House, saying, “it could happen, could happen.”