“More money does not necessarily mean more help for anyone,” the governor said last week. Addressing reporters on Monday, he added: “My point has been, the old Albany equation as a progressive — ‘The more money you spend on something, the better’ — no! ‘Well, if we spend more, we’ll accomplish more.’ No!”

But Mr. de Blasio, whose inauguration will take place at City Hall on Jan. 1, is fast becoming a national liberal leader whose views will be difficult to ignore. He headlined a delegation of newly elected mayors who met with Mr. Obama at the White House last week, and emerged saying the mayors, one after another, had talked about the same issues, like fighting inequality and poverty, and expanding access to early childhood education.

“There’s a progressive movement in this country that’s having a real effect,” Mr. de Blasio said. “Hearing each of my colleagues lay out what happened in their elections, what their vision was, the passion they felt — it’s clear that something is happening around this country, and that the inequalities we’re facing are becoming just fundamentally unacceptable.”

Mr. de Blasio not only is seeking to raise taxes, but also has pledged to champion several proposals favored by liberals that Mr. Cuomo has so far kept a conspicuous distance from. Those include granting driver’s licenses and state tuition assistance to undocumented immigrants.

The structural obstacles to liberals in New York are considerable. Some prominent elements of Mr. de Blasio’s agenda — such as his proposed tax increase to pay for expanding prekindergarten and after-school programs — would require approval from Albany. And even though Democratic voters outnumber Republican voters in the state by a ratio of two to one, Republican legislators represent large parts of the state, and they control the State Senate in a coalition with a small faction of breakaway Democrats. Republicans also held on to the county executive positions in several large suburban counties last month.

Needless to say, right-leaning political leaders are not enthusiastic about the agenda advanced by Mr. de Blasio and his allies.