WASHINGTON--The Democratic presidential candidates on yesterday found themselves stuck in a logjam of delegates that left none of them likely to lock up the party's nomination by the end of the primaries.

"Mathematically and politically this process is in gridlock," said Terry Michael, spokesman for Sen. Paul Simon (D.-III.), who suffered a shutout in Super Tuesday's round of primaries and caucuses.

Simon, who held just 35.5 delegates both before and after Tuesday's balloting, can only hope that nobody will have gained the 2082 delegates needed to win the Democratic presidential nomination. The primaries conclude on June 7, when California and New Jersey vote. The two states are among the largest, with a total of 423 delegates at stake.

Magic Number

"The person or persons with the greatest potential to negotiate his way to a first-ballot victory will be the candidate who is hottest at the end," Michael said.

The odds are growing longer that any candidate can come up with the magic number needed to win on the first ballot at the Democratic convention in Atlanta.

The Democrats have yet to allocate 2524 of their national convention delegates, and another 258.65 delegates list themselves as uncommitted. Thus the available pool of delegates to be won between now and early June would be 2782.65.

Massachusetts Gov. Michael S. Dukakis, who was leading the field of Democratic candidates with 456.5 delegates, needs to win another 1625.5 delegates to wrap up the presidential nomionation. Or, put another way, he has to win more than 58 percent of all the delegates that are still left to be won--roughly twice as well as he's done so far.

Dukakis was followed in the delegate count by the Rev. Jesse Jackson with 395.55 and Sen. Albert Gore Gore, Jr. '69 (D.-Tenn.) with 346.8.

The three-way tie in the Democratic race prompted former President Jimmy Carter to observe, "I think it's accurate to say the chances are less likely that one of the candidates will arrive in Atlanta with a clear majority."

Michael said if no candidate holds a majority by the time the primaries conclude, the rule of conscience that binds delegates to the candidates will begin to bend and break.

However, Jude Barry, an aide to the presidential campaign of Rep. Richard Gephardt (D.-Mo.), disagreed, saying, "I think there's going to be loyalty and commitment. We're prepared to protect what we have, as I'm sure the other candidates will as well."

Gephardt, who had 143 delegates after Super Tuesday, is hoping to hang on with a strong showing in the Michigan caucuses on March 26 and the congressional Democratic caucuses on April 19 and 20. Gephardt is planning on winning big when his House colleagues pick 210 of their own to be national convention delegates. Another 43 delegates will be picked by Senate Democrats.

Meanwhile, Republican resistance to Vice President George Bush's bid for the White House began crumbling yesterday as the impact of his fabulous Super Tuesday showing sank in.

Bush spent the day in Houston savoring his 16-state primary sweep and the roughly 600 delegates they brought. The outlook for Illinois wasn't bad either, as Gov. James Thompson was backing the vice president and Sen. Bob Dole (R.-Kan.)'s own campaign polls gave Bush the lead.