Donald J. Trump’s campaign was teetering early last month, with an increasingly isolated candidate and a downcast staff that seemed to lurch from crisis to crisis. Having fired his campaign chairman and retooled his message, Mr. Trump was still far behind Hillary Clinton in the polls, and Republicans were running away from him.

Under those desperate conditions, Mr. Trump’s closest allies last month pressed him to approve a daring plan: Go to Mexico and meet with President Enrique Peña Nieto, presenting himself to the world as a statesman and earning a new look from millions of American voters.

But the political gymnastics involved in Mr. Trump’s gambit will likely be difficult to sustain: His approach involves avoiding discussion of his former campaign pledges without renouncing them, and making ostentatious gestures of conciliation toward Hispanic voters and Mexicans without withdrawing — and at times actually repeating — remarks that have offended them in the past.

In the space of a few hours on Wednesday, Mr. Trump veered from avoiding a clash with Mr. Peña Nieto over his proposal for a border wall to goading an Arizona crowd into chants about constructing the barrier.