President Trump and Gov. Janet Mills of Maine have history.

When he visited the state early in the pandemic, he insulted her public health policies and called her “a dictator” who “doesn’t know what she’s doing.” The governor, a Democrat and brusque former prosecutor, did not mince words in response: “I have spent the better part of my career listening to loud men talk tough to disguise their weakness,” she said at the time.

It seems likely, given Mr. Trump’s long memory for slights, that he had not forgotten her appraisal in February when he tossed out a seemingly offhand question in a White House meeting with governors: “Is Maine here?”

The ensuing clash between the two leaders, over a Maine anti-discrimination law that allows transgender athletes to participate in girls’ and women’s sports, has escalated steadily since then. After Mr. Trump threatened that day to cut off funding for Maine, and Ms. Mills shot back, “See you in court,” she has not budged from her stance: that complying with the president’s executive order barring transgender women from women’s sports would violate the Maine law.

While she has stood firm, the federal government has barraged the state with investigations, declared its education system to be in violation of federal law and frozen some of its funding.

The Department of Education has set Friday as a final deadline for Maine to comply with the president’s order. If it does not, the agency plans to hand the matter over to the Department of Justice for enforcement.