Washington — Reagan campaigners are quietly cheering as the Democrats cut up one another in the race for the presidential nomination. Sen Gary Hart's challenge to Walter F. Mondale keeps Democratic attention off President Reagan and delays the time when the political battle is joined.
''The Democratic Party will have a fight and that suits us,'' says a key Reagan adviser. ''It helps us because the Democrats can't focus on the President.''
GOP political strategists say they are sanguine that Mr. Reagan could defeat either Mr. Mondale or Senator Hart in an election. They have adopted a wait-and-see attitude before making any changes in campaign strategy, and they are awaiting the outcome of the Super Tuesday primaries before beginning their polling of public attitudes.
But Mr. Hart's unanticipated surge - if it culminates in a victory at the Democratic convention - would pose a new challenge for the Reagan reelection campaign. Political experts say a number of factors would have to be taken into account:
* Hart could move toward the political center more quickly than could Mondale - a center that Reagan must also seek to co-opt.
* The youthful Hart might be able to make age an issue and, if he said the right things, keep the Democratic support of senior citizens.
* Hart has so far demonstrated strongest support among independents - the group that Reagan captured in 1980.
* Hart could force Reagan into a discussion of the issues and point up his weaknesses, something Mondale has not yet succeeded in doing.
* As a Coloradan, Hart could make some inroads into the West, now firmly Reagan territory.
Such factors are hypothetical, of course. Mondale, while he seems to be in a ''free fall,'' as one GOP campaigner puts it, is not yet out of the race and could make a strong comeback.
But as Reagan strategists look ahead to a potential Hart sweep, they will have to reevaluate campaign tactics and strategy in the light of new factors, experts say.
''There are significant differences in the two races (Hart-Reagan and Mondale-Reagan),'' says John P. Sears III, a former Reagan political strategist. ''Mondale is a known commodity and that race was a 'book race.' You knew where you could do well. Mondale could exploit everything and still come up at only 47 percent (public support).''
''In a race with Hart,'' says Mr. Sears, ''if you keep your hat you can still beat him, but you can't tell. Mondale is an identity that is allied with special interests and postured where he would have to move toward the center. So Reagan could occupy the center himself and be secure. Hart is on the crest and drawing votes from all directions and you're not sure what his identity will be.''
Republican officials stress that political judgments are premature. While Hart has momentum at the moment, based in part on his charisma, they say, his appeal could wane once the public begins probing his record, ideas, and character. Questions are already being asked as to why he has let the impression stand that he is a year younger than he actually is and why he changed his name from Hartpence to Hart. Even if Hart emerges the front-runner, Reagan campaigners say, the President will conduct the same kind of campaign - linking the Democratic candidate to failed liberalism and emphasizing the President's record.
''Mondale, Hart, and McGovern are three peas in a pod, and we don't see 5 percent of difference between them on the issues,'' says an official at the Reagan-Bush '84 reelection committee. ''If the Democrats deprive us of being able to tie the Carter tin can to Mondale, we'll tie the McGovern tin can to Hart. We'll also get it out that the last time Caddell advised a candidate, we did not have a successful presidency.'' Hart was McGovern's campaign manager in 1976 and pollster Patrick Caddell is now advising the Hart campaign.
As Reagan operatives see it, Hart would have problems running against Reagan for two reasons: One, the Democratic Party is seen as stagnant, whereas the GOP is viewed as providing the ''new ideas'' that Hart now says the country needs. Second, the American people are ''hungry'' for a successful, two-term presidency that can heal the wounds of so many one-term presidencies.
''Hart is coming out of a left-field candidacy that Jimmy Carter also represented in 1976,'' says a GOP campaign official. ''I don't think people will buy a pig in a poke.''
''Running against Hart is harder only because we don't know that much about him,'' says Charles Black, a consultant to the Reagan campaign. ''We planned on Mondale. But we don't mind running aganst Hart. He's very liberal on foreign policy and domestic issues. He's also an 'experience issue.' What's he done? He has no executive experience and no legislative accomplishments. People are looking for leadership, and that's Reagan.''
Mr. Black also suggests that Hart could not match Reagan's charisma, that such a youthful candicacy would probably drive elderly voters back to the Reagan camp, and, although Hart would make Colorado more competitive, he would still be beaten in his home state. Another factor, he adds, is that organized labor will not adapt to Hart and may go after him - even trying to generate a Kennedy boom at the convention.
For his part, Mr. Sears, who was let go from the Reagan team in 1980, says that issues are often overvalued and that voters tend to look at the individual.
''Voters will trust a man to be president even if they disagree with him,'' he says. ''Mondale did not have the flair or presence to compete on that level. Now we have to wait and see about Hart.''
''Hart is part of a different syndrome from Mondale,'' Sears adds. ''Nonideological voters, none active in the party, are drifting back into the system, and Hart is a demonstration of that.''