Last week -- the Week of the Debates -- shook Republicans' euphoria about the prospects of a runaway election victory, but it did not drastically damage President Reagan's advantage over Walter F. Mondale in measurable political strength.

It did, however, create a psychological climate in both the media and public opinion that makes next Sunday's second Reagan-Mondale debate clearly the crucial event in the whole campaign, and almost a must-win affair for the incumbent.

Strategists in both parties said that after six weeks of breezing through his reelection campaign with a minimum of pressure, Reagan now faces greater scrutiny and tougher standards than anyone else on the national tickets.

Vice President Bush and his opponent, Rep. Geraldine A. Ferraro (D-N.Y.), passed their big test on Thursday night by scoring enough debating points to convince the backers of each slate that their contender had won.

Mondale delighted all of his supporters and astonished many skeptics by dominating Reagan in their domestic policy debate last Sunday. Only the president -- whose prowess had been assumed by many -- still needs to prove his mettle in the televised forums that have unofficially, but efficiently, predicted the winner of every election in which they have occurred.

Tracking polls by both parties showed that the gains Mondale achieved in the first 72 hours after the debate began to level off this weekend, with Reagan still well in front. The main effect of the sharp improvement in perceptions of Mondale as a person seems to have been the shift of weak Democrats -- previously bothered by his personal qualities -- from the undecided colmn into the Mondale ranks.

Newspaper surveys taken since the first debate show such normally Democratic states as Maryland and Massachusetts moving toward their historical alignment. But Robert Teeter, whose company is polling for Reagan in several traditionally Democratic midwestern and northeastern states, said, "I still don't know of one state that is safely in his [Mondale's] grasp."

Peter D. Hart, Mondale's chief pollster, said, "Obviously, when you are 13 points behind, you want it to move, but I don't think it will move much until the shootout in Kansas City," where Reagan and Mondale debate next Sunday.

Robert G. Beckel, Mondale's campaign manager, said Friday, "We'll go into the second debate about 10 points down," and Republican strategists are fully prepared for the next round of public polls due this week to show Mondale's share of the vote climbing into the mid-40 percent range.

Richard B. Wirthlin, the top Reagan pollster, said the late-week stabilizing in the polls indicated that "both men are so well known, that even a perceptual loss for the president did not translate into a shift in vote commitment."

Wirthlin also made the point that the differences in political philosophy and program -- articulated more clearly by Bush than by Reagan -- still seem to cut in the Republicans' favor. It was notable that Reagan returned to those basic differences in his stump speeches Friday, dwelling on the contrasts between his record and that of the Carter-Mondale administration as he whistle-stopped through Ohio on what some observers judged a particularly effective campaign day.

But Republicans acknowledge privately that last Sunday's debate did introduce a new issue -- the question of Reagan's age and competence -- which will surely grow in importance if Reagan does not eliminate it by a stronger performance in the next debate, which will concern foreign policy.

"Louisville erased a lot of question marks behind Mondale's name," said pollster Hart, "and put a big one behind Reagan's. That has to be helpful to us."

A study of media coverage by John E. Merriam, which appeared in the Issues Management Letter issued Friday, found that the Democratic ticket had enjoyed an increasing edge in favorable stories in the two weeks leading up to the Louisville debate -- an edge Merriam said had widened greatly in the first half of last week.

Some Republicans strategists said they welcomed the Bush-Ferraro debate, if only because it shifted the focus, at least temporarily, from Reagan's supposed shortcomings. Stories about that debate -- in which Bush fared at least as well as Ferraro -- dominated Friday and Saturday's newspapers and television reports.

But most politicians expect that to be the last time the running mates upstage their principals. "That was their finest hour," said Republican consultant John Deardourff, "and their last. Bush can't do any more to help prop Reagan up, and I doubt that Ferraro will win many new votes for her ticket."

He, like others, said "there will be a tremendous amount of pressure" on Reagan next Sunday to "demonstrate that he is up to four tough years in a pressure-cooker job."

This week's scheduling almost seems designed to rebuild Reagan's self-confidence. He starts the week with a swing through the South, where the Claibourne Darden poll of nine states, released yesterday, showed no diminution in Reagan's 67 percent pre-debate share of the vote. Mondale climbed from 25 to about 30 percent after the debate, with all his gain coming from the undecided column.

On Thursday, Reagan will share the stage with Mondale at the annual Al Smith Catholic charity dinner in New York, an event that has special significance for him. It was the morning after the 1980 Al Smith dinner, where Reagan had overshadowed President Carter with a display of easy wit, that Reagan decided to debate the incumbent -- a decision that turned out to be the key to his victory.

White House aides are hoping that the dinner has a tonic effect on Reagan's optimism again this year.

They insist -- and most independent data tends to confirm their claim -- that nothing that has happened so far puts Reagan's reelection prospects in jeopardy. A half-dozen pollsters, working in about 18 states from Oregon to New England, were contacted by The Washington Post Friday and yesterday. The median gain they reported for Mondale from pre-debate levels was 3 or 4 points, and the median loss for Reagan 1 or 2 points. In few of the states -- New York, Massachusetts, Oregon -- was the Reagan margin down to single digits.

With the exception of one Democratic pollster who found voters in three states "coming off of Reagan," all of those contacted said that the shifts were mainly what one called "embarrassed Democrats deciding they could support Mondale after all."

Beckel, acknowledging that the "weak Democrats" he said have shifted to Mondale in the past week are easier to move than the independents, said he did not "expect them the independents to move until after the second debate."

Nonetheless, the pickup has had important psychological and political benefits for the Democrats. New York Gov. Mario M. Cuomo (D) spoke in an interview of "the electricity" in the crowds for Mondale and Ferraro last Monday. "Democrats are saying, 'Thank God, we thought it was all over,' " he remarked.

Across the country in Sacramento, California Assembly Speaker Willie Brown (D) said, "The loyalty factor and the willingness-to-participate factor went up dramatically on Mondale's side after the debate. He's moved himself from being a liability, to being respectable. They're not embracing him yet, but that will come."

Mondale and Ferraro will be campaigning heavily this week in California, in part because it is the only one of the major Sun Belt states where they appear to be at all competitive. Florida is far out of reach. And while Texas Gov. Mark White (D) spoke of the "momentum moving our way" in Texas, others who know the state well are less optimistic. Former Democratic national chairman Robert S. Strauss said from Dallas, "It's developing into an interesting situation, and we might yet have a chance. But we're not there yet."

Two border-state Republican governors, Christopher Bond of Missouri and Lamar Alexander of Tennessee, said conservative Democrats in their states appear to be staying with the president. Bond, fresh back from the "Little Dixie" part of his state, said, "Some folks were concerned about Reagan's style in that debate, but they still agree with him on the issues."

Republican National Chairman Frank Fahrenkopf said from Reno that "we always assumed it was going to be a close election. That's why we went out and registered 3.2 million new Republicans."

But a Gallup Poll released today had good news for the Democrats on both registration and turnout questions. It showed that the registration efforts of both parties and of independent groups have increased the registered voter share of all persons interviewed in three late-summer surveys from 70 percent in 1980 to 74 percent this year. Also, the "turnout index," based on the firmness of voting intentions, has increased from 49 to 53 percent.

The sharpest gains came among self-described Democrats. They went from 74 to 78 percent on the registration question, while Republicans climbed from 78 to 80 percent. The "turnout index" was even better for Democrats, climbing from 51 to 58 percent, while the GOP stayed at 60 percent.

The sharpest increases in both registration and stated intention to vote came among blacks, who added 10 points to their registration number and 17 points to their "turnout index." If the poll is accurate, blacks are likely to vote in larger proportions than whites -- a reversal of the pattern in 1980 and earlier years.