The plunging stock market reverberated like a clap of thunder through the Republican political community yesterday, raising the prospect of an election campaign conducted against the backdrop of shaken confidence in the economy or possible recession, eroding the party's single most valuable theme of continued prosperity.

Democrats were quick to pin the blame on President Reagan's policies, but some of the most worried voices came from within the GOP itself, where political analysts, pollsters and economic specialists said they could only hope the market rebounds and the economy does not slip into a downturn as the 1988 presidential campaign intensifies.

"This is a shot across the Republicans' bow," said Lawrence Kudlow, chief economist for Bear, Stearns & Co. and a former Reagan administration budget aide who has been advising the campaign of Senate Minority Leader Robert J. Dole (R-Kan.). "I think the stock market crash today raises serious questions about the economy, and since economic growth and job creation has been a strong Republican issue, it could be that even that will turn sour before long," he said.

Referring to the record-breaking trade and fiscal deficits of the Reagan years, Kudlow added, "These are Republican deficits whether the party likes it or not. They cannot blame {former House speaker Thomas P.} Tip O'Neill or Jimmy Carter. The stock market is a clear shot across the bow -- a warning."

"My sense of it is that any uncertainty -- and this creates uncertainty -- in the economy gives the Democrats an opportunity to go out and really try to exploit the weaknesses in the Reagan program," said Ed Rollins, the veteran Reagan political adviser who is now advising Rep. Jack Kemp (R-N.Y.). "The bottom line is that it's got to hurt us," he added, noting that continued confidence in the economy was a bedrock element of all the Republican candidates' hopes for the White House.

"This kind of a blow today is going to shake that confidence," he said.

Richard Whalen, an author and international consultant, attributed the stock market crash to a sense that the nation is leaderless at a critical juncture. "Who's in charge?" he asked rhetorically. "We're in the presence of a total panic and stampede. It's bad for incumbents and good for outsiders." Another veteran Republican analyst said, "Today's drop . . . raises questions about the future of the recovery." He noted that almost all the markets' gain this year had evaporated. "This could be a huge withdrawal of wealth from middle class and upper middle class people," he added. "This has got to be very worrisome."

Late in the day President Reagan made himself available to answer shouted questions from reporters while a noisy helicopter waited in the background to take him to Bethesda Naval Medical Center to visit his wife, Nancy. This was apparently an effort to restore confidence after the bottom fell out of the Dow Jones Industrial Average in the final hours of the trading session. "There is nothing wrong with the economy," Reagan said as he left the White House. "I don't think anyone should panic because all the economic indicators are solid."

Asked what he would tell a "little old lady who lost money today" in the stock market, the president replied: "I don't know of anyone -- are you talking about a specific case? Wait a minute -- how about how many people must have sold out in order to get a profit? Because they bought it back before it was ever this high."

Chief of staff Howard H. Baker Jr. telephoned investment bankers and others for advice about the market slide, but no crisis meetings were called. Last night officials said the administration was taken by surprise by the suddenness of the late-afternoon collapse of stock prices after a brief, late-morning rally.

Baker's predecessor in the White House, Donald T. Regan, a former chief executive officer of Merrill Lynch, said Reagan should "get in all the culprits, the heads of stock exchanges, and hear what they have to say, and then take some action."

Democrats responded to the events with a chorus of complaints about Reagan's fiscal and trade policies. "We are in the midst of a grave fiscal and political crisis," said former Arizona governor Bruce Babbit. "The economic chickens are finally coming home to roost."

Congressional Democrats urged Reagan to meet with them and break the longstanding impasse on the deficit. "It is time for the administration to begin working with the Congress to reduce the double deficits in trade and the budget that cast such a cloud on the nation's future," Senate Majority Leader Robert C. Byrd (D-W.Va.) said.

Rollins predicted that the political advantage would go to those who can capitalize on what he described as the "leadership void at both ends of Pennsylvania Avenue -- whoever steps forward first and looks in charge and has some sort of solution can once again get at the head of the curve."

Dole pointed to his own efforts in the Senate to reduce the deficit, but he added, referring to both parties, "I don't think any of us can escape the fallout from this."