In Iowa, Democrats are running ads attacking Senator Joni Ernst, the incumbent Republican, over her vote to repeal the health law. In Alaska, the Republican incumbent, Senator Dan Sullivan, is facing a tougher-than-expected challenge from a doctor named Al Gross, who is running as an independent but has been embraced by Democrats.

At least one Republican lawmaker — Representative Tom Cole, Republican of Oklahoma and a member of House leadership — conceded that the pandemic has made the electoral terrain for his party more challenging. He said he agreed with Mr. White, the strategist, that now may not be the best time to talk about the repeal.

“Yeah, people are very worried about any kind of change in the middle of a crisis, there’s no question about that,” Mr. Cole said in an interview. “On the other hand, ask Americans: ‘Are you really happy with the health care you’ve got? Do you think it’s reasonably priced?’ and the answer is inevitably no.”