The source of the friction was Mr. Cuomo’s handling of the proposed special session. The governor, perhaps overconfident that legislators would cancel holiday plans to secure their first raise since 1999, tried to tie the session to a few choice items of his own: an ethics overhaul, measures related to bias crimes and homelessness, and a plan to deliver app-based ride-hailing services like Uber and Lyft to upstate New York. (He had previously given up trying to extract more comprehensive ethics changes, among them instituting term limits and remaking the Legislature as a full-time institution.)

But as Mr. Cuomo begins positioning himself as a national leader of the left, it is his fellow Democrats who are most resentful of his maneuvering. In the telling of liberal activists, who hope New York will become a left-leaning bulwark against Mr. Trump, Mr. Cuomo has made only a watered-down effort at establishing a solid Democratic majority in the State Senate.

After the 2016 elections, the number of elected Democrats edged past the number of elected Republicans in the chamber. But because of a breakaway faction calling themselves the Independent Democratic Conference — and an even more independent Democrat, Senator Simcha Felder of Brooklyn, who has resolutely attached himself to the Republicans ever since being elected as a Democrat — the chamber has been controlled for several years by a coalition of Republicans and independent Democrats.

Neither Mr. Felder nor the independent Democrats budged after the November elections, drawing more accusations of Trump-enabling from liberals across New York. (In fact, the number of independent Democrats grew, and the group confirmed on Monday that it would remain happily coupled with the Republicans.)

Still, as vinegary as the talk has been so far, it is not hard to imagine the governor and Legislature getting over their differences in a few weeks as a matter of practicality. The governor’s tuition proposal is likely to find fans among a wide cross section of legislators, many of whose districts host community or four-year state colleges, and the issue of college affordability is politically potent.

“Once you get past all the venom and the vitriol and the bruised feelings, there’s a mutual self-interest in eventually finding agreement,” said Bruce N. Gyory, an Albany-based political consultant. “But it won’t be done with hearts and flowers, that I can assure you.”