As Donald J. Trump’s criminal trial wrapped up in May, one of his lawyers wanted to give the jury unusual instructions that would have made it harder to convict him. A special case warranted special rules, the lawyer argued, and the first prosecution of a former American president was “obviously an extraordinarily important case.”

The judge, Justice Juan M. Merchan, was unmoved. “What you’re asking me to do is change the law, and I’m not going to do that,” he said.

Justice Merchan has made a steadfast effort to approach the landmark case no differently than hundreds of others he has overseen.But more than three months after a Manhattan jury convicted Mr. Trump on 34 felony counts of falsifying records to cover up a sex scandal, the veteran judge faces his greatest predicament: He must decide whether to sentence Mr. Trump as planned on Sept. 18 or wait until after Election Day, as Mr. Trump has requested.

Justice Merchan has already agreed to delay the sentencing once, and his upcoming decision — which will be made in the heat of a presidential campaign that has pitted Mr. Trump against Vice President Kamala Harris — will reverberate well beyond his Lower Manhattan courtroom.

The decision could influence not only the election, but American politics for years to come. And it will almost certainly subject Justice Merchan to partisan second-guessing at a time when the nation’s faith in the judiciary has been shaken by the Supreme Court’s decisions on abortion, guns and other issues, as well as revelations about some of its justices’ own political entanglements.