The debate advisers of President Carter and Ronald Reagan argued over the time and place for the presidential campaign's single, crucial head-to-head meeting for 4 1/2 hours yesterday to no conclusion.

The Republicans proposed an election-eve debate and the Democrats held out for Sunday, according to James A. Baker III, Reagan's senior adviser at the debate negotiations.

While the disagreement over a date appeared to be a serious sticking point, with each side seeking what it considers politically advantageous timing, the dispute over location seemed rooted only in logistical concerns.

Both sides expressed confidence that there would be a quick resolution of the debate arrangements, and Ruth Hinerfeld, head of the League of Women Voters Educational Fund, the debate's sponsor, told reporters she expects a final decision within 24 hours.

The Carter-Reagan confrontation, coming so close to Election Day in a race generally conceded to be extremely close, has taken on the aspect of a winner-take-all roll of the dice for the two candidates, who have been campaigning doggedly since last year.

The league last week invited Carter and Reagan to debate Oct. 28 in Cleveland, after having abandoned its earlier position that independent candidate John B. Anderson should be included. The league excluded Anderson after reevaluating his candidacy.

Carter has been seeking a head-to-head debate since Labor Day, and Reagan responded to the league's new invitation -- and his polls showing his lead over Carter dwindling -- by reversing his stand and agreeing to meet Carter in a two-man debate.

The two sides spent much of their meeting yesterday discussing the debate's format, and reached all but final agreement, Baker said. The debate will allow follow-up questions, he said, but he refused to discuss further details.

"I have only one thing to check on and that's a date," Baker told reporters who asked if he had to discuss yesterday's meeting with Reagan. Baker said the Reagan campaign prefers Washington as the debate site because it is easier for them to detour here in the last days of the campaign.

On the question of a date, Baker said "we really like Nov. 3." He added: "About 10 percent of the people make up their minds on the election eve; let them make their decision on the basis of the debate." Baker said an election-eve debate could become an American political tradition.

The Carter representatives objected that an election-eve debate would leave no time for correction of any slips or errors before people vote. Baker conceded that it also would eliminate any media analysis of the debate that could influence voters by suggesting which candidate had "won" the debate.

However, Baker appeared to acknowledge that a new political tradition is not being born. He said that the Reagan side's fallback position had been any date from Oct. 28 to Nov. 3.

It appeared that the question of a vice presidential debate did get settled yesterday. There won't be one. Richard Moe, an aide to Vice President Mondale, left the meeting at the league headquarters early because he said the Republicans would not agree to a Mondale-George Bush debate despite Mondale's readiness to meet "anytime, anyplace."

Robert S. Strauss, chairman of the Carter-Mondale Reelection Committee, declined to comment on the meeting and urged Hinerfeld not to take questions from reporters after the session broke up. Strauss said, "we have something in the works," but added, "there are a lot of things to work out."

Despite the length of the meeting and the lack of a conclusion, Strauss and Baker said progress had been made and called the meeting constructive.