It seems at times like a rerun of "Crossfire," cable television's long-running ideological sparring match.

On the right is the familiar and feisty Patrick J. Buchanan, the combative and articulate spokesman of American conservatism. Substituting for Tom Braden on the left is the new voice of liberalism, Mario M. Cuomo, the charismatic and eloquent governor of New York.

The topic: the Reagan administration's proposal to eliminate the federal deduction for state and local taxes.

In the latest round of this unusually bitter and personal exchange, Buchanan, the new White House communications director, in a letter to the editor of The New York Times published yesterday, labeled Cuomo "the glib, fast-talking lobbyist for a reactionary liberalism that would kill tax reform in its crib."

Replied Cuomo, through his counselor and chief spokesman Martin J. Steadman, "If Pat Buchanan can't keep the debate on a decent level, he really ought to get out of the kitchen." Cuomo was giving a commencement address at Stanford University yesterday and chose not to respond directly to Buchanan's salvo. The response from the governor's office in Albany seemed somewhat restrained, given the strong language of Buchanan's June 13 letter. In it, Buchanan said that after Cuomo's "Trash America tirade" speech to the 1984 Democratic National Convention, "I never anticipated much in the way of decency or accuracy from the commentaries of Mario Cuomo."

Buchanan continued, "Mario Cuomo's incessant invocations of the poor, the downtrodden, the ill, almost invariably turn up as preambles to budget requests that would augment the power of his own political class -- the welfare statists."

This verbal back-and-forth between two of the most eloquent pontificators in American politics has become a somewhat curious sideshow to the debate over tax reform. It is an unusual dialogue between high-ranking public officials -- one touted as a future presidential nominee -- strewn with the kind of hyperbole and insults seldom seen in policy debates.

Buchanan's comments were the most forceful since his joining the White House four months ago. The former columnist and commentator initially tried to adopt a quiet, behind-the-scenes posture there.

Buchanan lately has been forced to adopt a more visible profile to respond to critics. He has dropped his policy of not returning reporters' telephone calls, and he told the Associated Press in an interview that he is setting up a "response desk" to return the fire when President Reagan is attacked.

Buchanan said yesterday his letter on Cuomo was not the first offensive from his "response desk" but was rather "to set the record straight." Buchanan was responding to Cuomo's June 8 news conference, in which the governor proclaimed that the Reagan tax plan smacked of "transparent demagoguery, which, if it does not set a new low, is certainly a tough record to beat."

Cuomo, in that news meeting, was responding to remarks Buchanan had made two days earlier on the tax package to economics editors. Buchanan had said the proposal to eliminate the deduction for state and local taxes would be strongly opposed by "the Democratic Party on the Mario Cuomo side."

Buchanan then defended the tax plan as fair, saying the philosophical goal behind lowering the top rate was to encourage investment rather than enact "wealth redistribution." He said, "If you get into this neosocialist concept -- are we trying to redistribute wealth? No."

That drew a strong response from Cuomo, whose state has the highest combination of state and local taxes in the nation, according to most surveys. "The president's spokesperson's stunningly irresponsible castigation of all states struggling to meet their needs as 'neosocialist' . . . is unworthy of the White House," Cuomo said.

He said Buchanan's "inveighing against neosocialism is wrong, insulting, unfair and denigrating to the entire state."

Buchanan in a telephone interview called Cuomo's news conference remarks "intemperate" and said they necessitated the strong response in his letter.