Mr. Trump’s strategy for keeping Congress in Republican hands has been to excite his base to turn out at the polls in close House and Senate races. That has meant — more than any other issue — pushing his hard line on immigration, whether by accusing Democrats of trying to “infest” the country with illegal immigrants, or by threatening to shut down the government over money for “the wall.”

But Mr. Barletta’s campaign is lagging far behind Mr. Casey’s in the polls and in fund-raising, even though he is one of the biggest immigration hawks in Congress. His struggles illustrate how Mr. Trump’s lightning-in-a-bottle victory may not be easy to duplicate this year in swing states like Pennsylvania.

Mr. Barletta is one of several Republican nominees closely aligned with Mr. Trump who do not appear to be getting much benefit from his endorsements in their general election races. Others include the Senate nominees in Virginia (Corey Stewart, known for defending Confederate monuments) and in West Virginia (Patrick Morrisey, the attorney general and a former pharmaceutical lobbyist).

Their difficulties suggest that, while Mr. Trump’s blessing can be crucial in winning a primary, hugging him closely in a general election race can be counterproductive for some Republicans, pushing away independent voters and firing up Democrats who are burning to rebuke the president this fall.

Mr. Trump was able to carry Pennsylvania — something no Republican presidential nominee had done since 1988 — because places like Westmoreland County, which includes Youngstown and the Trump House east of Pittsburgh, voted for him in huge and unexpected numbers. He won the county, a mainly exurban and rural area that was once a blue-collar Democratic stronghold, by 31 percentage points, a wider margin than in any other major county in the state.