Nashville — President Reagan and his Democratic opponent, Walter F. Mondale, may continue to spar over whether new taxes are needed to curb the growing federal deficit. But if they were to heed the advice of the nation's governors from both parties, they'd give up the fight and concede that higher taxes must be part of any solution.
Some Republican governors in this election year raise the revenue issue only softly and as a last resort. For instance, Illinois Gov. James R. Thompson, a Republican and Reagan supporter, says he supports the President's pledge to make all possible spending cuts first and to consider tax changes only as part of a tax reform package.
But Vermont Gov. Richard A. Snelling, also a Republican and co-chairman of Mr. Reagan's reelection campaign in that state, insists a tax hike is ''absolutely essential.''
And the largely Democratic National Governors' Association (NGA), whose members are meeting here, has been firmly on record since February in support of a plan to raise federal taxes by 5 percent and sharply cut spending across the board over the next five years.
No governor here is suggesting that Washington money sent to the states be exempt from the cuts. ''Whether we like it or not, we're affected,'' says Kansas Gov. John Carlin (D), NGA chairman-elect.
Congress took action before its July recess to curb the rising deficit, but most governors here view it as a small step. ''They labored for months and brought forth a mouse,'' insists Governor Snelling.
''I hope we will not be lulled into a false sense of security - Congress can't afford to rest on its so-called down payment,'' says Utah Gov. Scott M. Matheson (R), who has been what the NGA calls its lead governor on the federal budget. In his view, such programs as medicare must be changed to make eligibility dependent on need. ''Medicare is the biggest unleashed, unmanaged piece of spending in the US today,'' he says.
Many of these governors have raised taxes in their own states without losing elections. ''I don't think it's always political suicide,'' says Maryland Gov. Harry R. Hughes (D), who raised gasoline taxes in his state during an election year. ''I really think people would rather you be straight with them.''
The deficit is not on the formal agenda here in what residents and welcoming banners call ''Music City USA.'' But it crops up regularly in almost every panel discussion and hall conversation.
Some, like Gov. Richard D. Lamm (D) of Colorado who insists he is known in his state as ''Mr. Gloom'' for his views on the subject, say they are concerned the issue will get lost in election-year politics.
''The only honest political platform is to say, 'We're going to cut services and raise taxes,' '' he says. ''But nobody wants to bite the bullet. We need to take a Churchillian blood-sweat-and-tears approach to what this society is going to have to do to get its economy in order.... (But) I think it's going to take an economic Dunkirk to make something happen.''
Early in the NGA program, US Sen. Howard H. Baker Jr. (R), who is not running for reelection, stopped by the meeting to deliver an impassioned plea for a bipartisan solution to the deficit problem and to urge governors to lead the way. ''We've got to find a way to depoliticize it (the solution).''
Vermont's Governor Snelling, who is not running for reelection, insists the political problem can be resolved if Americans realize how serious and immediate the economic threat is to their own well-being. He intends to try to get that message across by building a cross-party coalition. Come January, he will devote his full time without salary to Proposition 1, the organization he founded in March. He recently persuaded former presidents Jimmy Carter and Gerald Ford to serve as honorary co-chairmen.
Snelling says he is bothered by the tendency of both parties to blame each other when each deserves some of the blame. ''We are not serving our enlightened self-interest in this country. The ultimate test for a democracy is whether it can practice thoughtful self-denial.''