A Bruised Trump Faces Uncertain 2020 Prospects. His Team Fears a Primary Fight.

Several prominent Trump antagonists are actively urging other Republicans to take on the president, and a popular governor, Larry Hogan of Maryland, has indicated he is newly open to their entreaties.

.. Privately, some of Mr. Trump’s 2016 aides have said they are pessimistic about his path to 270 electoral votes after his party’s midterm defeats in states like Michigan, Pennsylvania and Wisconsin. An Associated Press poll on Wednesday showed that Mr. Trump’s overall approval rating had fallen to 34 percent, with his support among Republicans dipping below 80 percent — a startling turn for a president who strives for total control of the G.O.P., and has usually achieved it.

..An Associated Press poll on Wednesday showed that Mr. Trump’s overall approval rating had fallen to 34 percent, with his support among Republicans dipping below 80 percent — a startling turn for a president who strives for total control of the G.O.P., and has usually achieved it.

.. The Mueller investigation looms as another destabilizing force for the president. David Kochel, a Republican strategist based in Iowa who is opposed to Mr. Trump, said the special counsel’s eventual report could determine whether Mr. Trump is vulnerable in a primary.

“That will be a focusing mechanism for the party,” Mr. Kochel said.

.. Mr. Trump captured the presidency with a largely improvisational candidacy, guided by his own instincts for personal combat and cultural division, and lacking the strategic discipline of most presidential campaigns.

.. But even among his own political lieutenants, there is a general recognition that Mr. Trump currently lacks anything resembling a positive message.

.. Mr. Trump is especially fixated on two well-known Democrats, speaking frequently about Joseph R. Biden Jr., the former vice president whom Mr. Trump regards as his most dangerous potential opponent, and Senator Elizabeth Warren of Massachusetts. Some of his advisers are more preoccupied with two other would-be challengers, who would offer a starker generational contrast with the 72-year-old president: Senator Kamala Harris of California and Beto O’Rourke, the former Texas Senate candidate.

.. Now a top aide on Mr. Trump’s campaign, Mr. Stepien and his deputies have been consulting party leaders about shutting off avenues to a challenge and ensuring that states cannot put forward “favorite son” candidates to contest the president’s renomination.

.. Mr. Trump has also dedicated a team of aides to guaranteeing that only political loyalists are elected to serve as delegates to the convention. To that end, Mr. Stepien dispatched some of his staff members this month to see that their preferred candidate remained in charge of the Maine Republican Party.

..Mr. Hogan spoke briefly with William Kristol, an implacable Trump critic in the conservative press, who argued that the president is weaker than widely understood

.. In addition to Mr. Hogan, William F. Weld, the former Republican governor of Massachusetts, is weighing a challenge to Mr. Trump as a small-government moderate, people who have spoken with him said. Mr. Weld, 73, who was the Libertarian Party’s vice-presidential nominee in 2016, has discussed either opposing Mr. Trump in the Republican primaries or seeking the Libertarian presidential nomination.

.. Other Republicans known to be entertaining campaigns against Mr. Trump include John R. Kasich, the former governor of Ohio, who ran in 2016; Senator Ben Sasse of Nebraska; and Jeff Flake, the former senator from Arizona. But Mr. Sasse is said to have grown uneasy about the idea, and Mr. Kasich and Mr. Flake are pursuing opportunities in television.

.. Bruce Berke, a Republican strategist in New Hampshire aligned with Mr. Kasich, said he currently saw Mr. Trump as unassailable in a G.O.P. primary.

“A primary challenge in 2020, as of today, would be futile for anyone,” Mr. Berke said.

Still, Republican donors will want to know just how damaged the president may be by the end of this year before they truly commit to a challenge.