Flush with funds but nervous that a weak economy yet may spring the trapdoor on many of their candidates, the custodians of President Reagan's shaky political coalition are hoping that election day 1982 arrives before public opinion pronounces a verdict of failure on Reaganomics.

As the ambiguous midterm campaign enters its final six weeks, Democrats are predicting -- and Republicans acknowledging -- the likely capture of GOP governorships in several major states.

But they are uncertain whether the multimillion-dollar Republican defense of incumbents can stalemate the drive by Democrats and their labor allies to break the president's narrow working control of Congress, or if there will be a Democratic stampede.

The Gallup Poll weighed in today on the side of stampede, with a survey saying that, if likely voters maintain their current preference for Democrats, Republicans will suffer "at least the normal loss for the party in control of the White House."

According to Gallup, that means that at least 30 of the 192 seats Republicans hold in the House of Representatives will be filled by Democrats next year. That shift would be enough to threaten Reagan's mastery of defense, domestic and budget policy in Congress.

If paralleled in the Senate, which history suggests would be the pattern, it might even put the Democrats back in control after a two-year hiatus. History suggests that it would also weaken the Republicans' 53-to-46 edge in the Senate but, barring extraordinary upsets, Democrats are unlikely to win five of the 12 Republican seats up this year, as they must do to regain the majority.

Few leaders in either party now expect such dramatic changes when what is certain to be history's most expensive midterm congressional campaign winds up Nov. 2.

The predictions are for a low voter turnout, which works against the Democrats. And lists kept by both sides of genuine battleground House and Senate seats have been growing shorter, not longer, as primaries have run their course and early general-election polls have been taken.

As of now, barely half-a-dozen Senate seats and scarcely two dozen House seats, about evenly divided between the parties, appear to be in serious doubt. That spells no landslide. But Republicans fear that could change quickly if October finds the country with its first double-digit unemployment rate since the Great Depression and voters decide that Reaganomics is a flop.

Right now, the only place where most political pros see a prospect for a genuine power shift is in the gubernatorial battles in the big states, where the combination of recession layoffs and budget squeezes could give the Democrats a major boost.

The Democrats' optimism rose after the announced retirement of five Republican incumbent governors in the upper Midwest: William G. Milliken of Michigan, Robert D. Ray of Iowa, Lee S. Dreyfus of Wisconsin, Al Quie of Minnesota and James A. Rhodes of Ohio, who was unable to run for a third consecutive term due to state law. All but Quie, beset by economic and budgetary problems, were good reelection bets.

The eight most populous states, with 225 of the 534 electoral votes, choose governors this year. Republicans control five of them, and only one of the five governors, Pennsylvania's Richard L. Thornburgh, is a clear favorite for reelection. Democrats are mounting major threats in Illinois and Texas and are favored, at this point, to take over in Michigan and Ohio.

The Republicans have a chance to reclaim governorships being vacated by Democrats in California and New York, but in both cases the GOP candidates are underdogs. In the last of the eight major states, Florida Gov. Robert Graham (D) seems in no danger.

The relatively glittering prospects in gubernatorial races are one reason Democrats are focusing their limited national party campaign funds on those battles. Democratic National Chairman Charles T. Manatt last week predicted only a 15-seat pickup in the House and either an even break or a two-seat gain for his party in the Senate. But he said a net gain of four or five governorships was well within reach.

Republican Party professionals talk even more optimistically about their chances in Congress, but mirror the concern about governorships. Rich Bond, the Republican National Committee's deputy chairman and political director, predicts a standoff in House seats and a two- to five-seat gain in the Senate, unless there is some sudden reversal of political fortunes in the next six weeks.

But Bond concedes that Republicans could have statehouse problems, not just in four of the five big states they hold but in such other gubernatorial battlegrounds as Nevada, Wisconsin, Arkansas, Oregon and Nebraska.

Minnesota has been on that list, too, but the odds may have changed after last Tuesday's primary when Republicans and Democrats dumped their convention-endorsed candidates and set up a Nov. 2 contest between former governor Rudy Perpich (D) and businessman Wheelock Whitney (R). No one has had time to assess the odds in that race.

Republicans trail Democrats, 27 to 23, in governorships, and with 10 of their own in jeopardy they need to beat the Democrats in some of their target states -- California, New York, Connecticut, Hawaii, Alabama, Kansas and Idaho -- to avoid starting the 1984 presidential race with a severe imbalance in statehouse political strength.

By contrast, very few Senate races look close at this point. Most incumbents in both parties, including some expected earlier to have problems, are sailing smoothly with poll leads of 20 points or more and healthy campaign budgets to sustain their television images.

About the only states where informed operatives of both parties agree that the Senate races are in doubt are California, Connecticut and New Mexico, now held by Republicans; Maine and Nevada, now held by Democrats, and Virginia, held by retiring independent Harry F. Byrd Jr. There may be a half-dozen more states with possible upsets.

There are several reasons for this. Many Democratic losers in the 1978 and 1980 elections were liberals from non-urban, non-industrial and more conservative states: Dick Clark and John Culver of Iowa, George McGovern in South Dakota, Frank Church in Idaho.

Another is chance: the sudden death of John Ashbrook, the Republicans' leading candidate in Ohio, and the revelation that Bruce Caputo, their strongest challenger to Daniel Patrick Moynihan in New York, had lied about his military service during the Vietnam war years, which forced him to drop out.

Yet another is the solid strength of the ideologically moderate Democratic incumbents in such Sun Belt states as Arizona, Texas and Florida.

One reason for the divergence between the Gallup forecast on congressional seats and that of most professionals who assess prospects state-by-state and district-by-district may be the calendar.

"There's always a trend," says Democratic lawyer James H. Rowe Jr., whose experience dates to Franklin D. Roosevelt's time. "Sometimes it shows up early, and sometimes late, but there's always a trend."

Agreeing with that judgment, Republican pollster Robert Teeter observed last week that "for most voters, the campaign is just now beginning." Only now are they beginning to hear the names and identify candidates' campaign themes.

In 1980, Teeter recalled, it was not until the second week of October that polling on individual House and Senate races began to show that the Republican trend would reach beyond the presidential contest and bring gains for the rest of the ticket. It is likely, he said, "we'll have to wait at least that long" for this year's races to crystallize.

That is one reason why many Republican operatives have circled Oct. 8 on their calendar. That is the day of the government's last pre-election unemployment report. With newspapers full of stories the last few weeks of layoffs and rising numbers of initial unemployment insurance claims, many of them fear that Oct. 8 will bring the bad news of double-digit joblessness, up from the last report of 9.8 to 10 percent or more.

Breaking that psychological barrier might, they fear, shatter what one GOP political strategist called the "extraordinary public patience" with Reaganomics and trigger a political revolt. So far, Republicans feel, they have suceeded beyond their dreams in bolstering the belief that the president's program "just needs more time to work."

Democrats agree. Private polls taken for their candidates have been showing in many states that while voters think they are worse off today than when Reagan was elected most still believe things will improve in the next two years.

For that reason, many Democrats are focusing on concerns of special constituencies -- the elderly, women, minorities, environmentalists and especially the unemployed -- rather than seeking a broad debate on economic policy. Two Democratic media advisers, with candidates in a dozen states, said last week that in none of their campaigns are they seeking a "referendum on Reaganomics."

"We talk about effectiveness one place," one said, "about fairness another, about imports in a third state, about farm prices in a fourth. We don't talk about Reagan or Reaganomics."

Republicans -- particularly their best salesman, Reagan -- are trying to make this a referendum on the economic future, believing that voters do not want to "turn back to the Democratic policies of the past," as they put it. But if today's Gallup Poll is correct voters may be preparing to turn the tables on the GOP.

The poll found a 56-to-44 percent preference for Democrats among the 1,190 likely voters interviewed in two national samples of 3,062 adults in polling in mid and late August.

In 1980, Democrats received 50.4 percent of the House vote nationwide and won 243 House seats. In 1978, they received 53.7 percent of the vote and won 276 seats. Now Gallup finds Democrats the choice of 56 percent of likely voters, and says that should mean a 30-seat gain.

Moreover, the survey suggests that one can probably bet on that outcome. Preference for Democrats essentially has been stable since February, after 1981 showings looked more favorable to the GOP.

The Democratic edge is found in all sections, ranging from 52 percent in the West to 54 in the Midwest, 56 percent in the South and 59 percent in the East. It conforms closely to earlier reported findings of summer polls by Louis Harris and David Garth, and to a separate Gallup Poll finding that, by 55-to-45 percent, voters say they think Democrats will do a better job on whatever problem those voters consider most pressing.

To no one's surprise, 48 percent of the voters name unemployment as the most important problem. That is a traditional Democratic issue, while inflation, on which Reagan and Republicans dwelled in 1980, has dwindled to a distant 23 percent in second place.

Finally, Gallup points out that figures in its September survey historically have been an accurate guide to the election outcome. Only once in the last seven midterm elections has the outcome been more than 1.5 percentage point off the September poll. In the three midterm elections of the 1970s the average deviation was less than 1 point.

In the face of that evidence and of academic analyses suggesting that the recession and decline in presidential approval ratings doom Republicans to an even larger 40-seat loss, there is a substantial body of opinion that sees Republicans surviving the midterm election with their congressional coalition essentially unscathed. Skeptics point to such factors as these:

* Republicans enjoy unprecedented financial advantage this year, with $146 million in party funds raised as of July 1, compared with $19 million raised by national Democratic committees. While individual Democratic incumbents usually are better financed than their challengers, the Republicans hope that late money from corporate and trade-association political action committees (PACs) will help them much more than labor and liberal PACs will aid the Democrats.

* Despite high unemployment and a generally low public rating of Congress, voters showed no disposition during the primary season to clean house of incumbents. No senators and only eight representatives seeking renomination were denied it, and five of those defeats were made inevitable by redistricting that forced incumbents of the same party to oppose each other.

A status quo election would be a satisfactory outcome from the point of view of Reagan and Republicans. In the euphoria of their 1981 legislative victories some Republicans talked of gaining strength in the midterm, a feat no party in control of the White House has managed since 1934.

Those hopes suffered a double blow. Instead of gaining seats from redistricting, as they had expected, Republicans barely managed a standoff with the Democrats. And the recession created a tougher economic climate for the November vote.

For the last year, the Republican congressional campaign committee has been preparing its House incumbents for adversity. Many of those in shaky, recession-weakened seats are freshmen and sophomores thoroughly versed in the modern techniques of mass mailings and mass-media politics.

Nevertheless, they have been coaxed and prodded to build their individual popularity and visibility, separate from Reagan's, for the challenge the fall of 1982 seems likely to hold.

While most of their Democratic challengers have been scrambling for their first $50,000 of campaign funds, these young incumbents have been drawing on party and PAC funds typically six to 10 times that amount

That is why some Republicans, such as Bond and congressional campaign committee executive director Nancy Sinnott, say they believe they can escape unscathed, despite the Gallup Poll and other forecasts.

Others would be happy to settle for the loss of 12 House seats that has been the average in the last two decades for the first midterm election after a change in control of the White House.

Right now, no one is sure what to expect. As Ed Rollins, the White House political director, observed Thursday, "This could be one of the most volatile elections we've ever seen -- a real Frazier-Foreman fight."

And the Gallup Poll suggests that, if that kind of fight develops, it will be the Republicans who are KOd.