Dr. Maguire, 59, and her husband, 74, have disagreed over politics before, but never like this. During the 2012 presidential campaign, they had two signs planted side by side on their front lawn in Belmont, Mass.: one for her choice, Barack Obama, and the other for his, Mitt Romney.

“Politics were very low on the list of priorities when we met,” said Dr. Stossel, whose political ideology made a rightward turn in the 1980s, bringing him more in line with his brother, John Stossel, who hosts “Stossel” on the Fox Business Network. “Therapists say you have the best relationships when you are clearly separate people. And I like to think that we are emotionally centered, so that we can have a major disagreement about something and it’s not a big problem.”

The couple avoided discussing the campaign into the summer, and Dr. Maguire, who said she will vote for Hillary Clinton, fell under the impression that her husband would no longer be supporting Mr. Trump. But in an interview on July 28, Dr. Stossel restated his support for the Republican nominee.

“I’m reasonably convinced that Hillary is handcuffed to the economic progressive populism that has totally taken over the Democratic Party, a.k.a., socialism,” said Dr. Stossel, a visiting scholar at the conservative American Enterprise Institute. “I think that if she gets power and the party gets power, there is a good likelihood that the agendas of that movement will be enacted. To me, that counters what I consider to be what brings us prosperity, which is entrepreneurship.”

When asked about Mr. Trump’s talk of building a wall along the United States-Mexico border and banning Muslim immigrants, Dr. Stossel said: “I think it is very unlikely that he can pull any of that stuff off. It seems improbable to me, because he still has to work in the constraints of what I hope will be a checks and balances system. Frankly, I don’t think he is going to have to make good on a lot of these crazy promises.”