Even as President Reagan put his new arms control proposal on the table in Geneva yesterday, influential Republicans here were saying that the ambitions of Democratic presidential hopefuls and the U.S. political calendar are reducing chances of a new nuclear pact with the Soviet Union in Reagan's first term.

"The electoral process may inhibit an agreement," said Rep. Richard L. Cheney (R-Wyo.), chairman of the House Republican Policy Committee and former chief of staff in the Ford White House. "It's conceivable that this debate will become so partisan you will get no agreement until after the election."

Cheney's assessment drew strong dissent from some Democrats and from Republicans more enthusiastic about the arms control process than he. But it was endorsed and strengthened by a senior White House official, who said he shared Cheney's view that Soviet leaders may be tempted to outwait Reagan in hopes that a more amenable Democrat will be in the White House in 1985.

The discussion, though low-keyed, suggested the explosive political potential of the nuclear arms control issue as the 1984 presidential campaign intensifies.

Cheney triggered the debate by observing at a breakfast with reporters that he is "concerned" by Democratic presidential hopefuls Walter F. Mondale, Alan Cranston and Gary Hart "committing themselves to running off to Geneva and laying a new proposal on the table" as soon as they take office.

"It's bad politics and it's bad policy," he said. All have said they would seek an early summit conference with Soviet leader Yuri V. Andropov on arms control if elected.

"There's no way that Ronald Reagan can outbid the Democrats, and it would be a mistake for him to try," Cheney said.

"From the Soviets' view, if it looks like the election is going to be a horse race, they may decide to wait and see if they get lucky and get Mondale or somebody like him to deal with."

Mondale said he rejected Cheney's view, because, "There is no more appropriate question for public debate than arms control . . . . The real impediment to such agreement is not free debate," he said.

"It is an administration that has given the impression to people in the United States and to our allies that it is not serious about arms control."

Cranston's press secretary, Murray Flander, said that "if Moscow is getting the message" Cheney described, "it's getting it from Ronald Reagan, not from what the Democrats are saying.

"Their the administration's actions speak a helluva lot louder than our words."

Former secretary of defense Clark M. Clifford said that what is impeding the arms talks is not the possibility of a Democratic president, but an "extraordinarily hostile climate" created by the hard-line rhetoric of the Reagan administration.

"It places an enormous burden upon negotiators when one side refers to the other as liars, cheats and the focus of evil," Clifford observed.

In a similar vein, Rep. Edward J. Markey (D-Mass.), a sponsor of the nuclear freeze resolution, said, "I don't think . . . the Russians would pass up a near-term opportunity to make a deal. There is a double risk. First, they can't be sure they're going to get a Democrat in 1985 , and then they have to wonder if any treaty a Democrat negotiates can be ratified. My sense is that Reagan is perceived . . . as the man best able, politically, to consummate a deal."

On the other hand, Rep. Jim Leach (R-Iowa), a strong arms control advocate, said, "There is a definite risk that the Soviets will . . . sit out serious arms negotiations until the election," but, like Clifford, he blamed that risk on administration "rhetoric which keeps rationality from coming into play."

Leach said Reagan's defense speech last week "scared the bejesus" out of people in Iowa.

But even before the latest round of discussion, some senior Democrats were expressing concern that their candidates' rhetoric was creating what one called "an agreement-at-any-price" posture for the Democratic Party.

And a high Reagan aide, who had heard of Cheney's comments, endorsed them, adding the further caution that serious negotiations were unlikely to begin until the fight over deployment of new U.S. nuclear weapons in western Europe is settled late this year, by which point the 1984 campaign will be well under way.

"There is no way the president can or should outbid the Democrats," he said, "and any agreement that looked like it was reached just for the sake of having a pre-election agreement would probably be a political liability, not an asset."