Voters in Tuesday's congressional elections appear to have spoken with two voices: keep the Republicans in the Senate, strengthen the Democrats in the House. However ambiguous it may seem, they have delivered a strong, consistent Election Day message.

They are telling both U.S. political parties they want changes made, and they are challenging the parties to do something about it.

The verdict at the polls thus adds up to something more than a desire for a correction in the nation's economic course. It calls for a new political partnership to address the country's serious problems.

"Both sides should do some serious soul-searching," said Peter D. Hart, a leading Democratic pollster, "and recognize the message the voters tried to deliver."

Hart cautioned Democrats not to think of their political victories in the House of Representatives and state capitols as a mandate. "Voters do not want to go back to the past," he said. "A simple and thorough assault on Ronald Reagan's program is not acceptable. Voters want a constructive kind of change."

There was no question, from the way key Republican and Democratic leaders in Congress responded to the election results, that the message was getting through. Talk of working to establish a period of compromise and conciliation, as opposed to stalemate and confrontation, was common in their public statements.

Other Democrats, from House Speaker Thomas P. (Tip) O'Neill Jr. (Mass.) to such potential presidential rivals as Sens. Ernest F. (Fritz) Hollings (S.C.) and Gary Hart (Colo.) were also speaking publicly about the need for more compromise and better cooperation on Capitol Hill. "I think we can compromise," O'Neill said.

He also said he was confident that Republicans felt the same way, and that they would help persuade President Reagan to go along with necessary changes. "I think they'll have enough influence on them to say, 'Listen, politics is the art of compromise. We're going to have to compromise on many of the things along the line.' "

Republican leaders in particular directly addressed that idea, and in so doing delivered a clear message of their own to President Reagan and the White House.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) made the point sharply, in a CBS television interview with Walter Cronkite, when he stressed the strong independence of the Republicans in Congress.

"I think that what happened in 1982," he said, "while it may have been a referendum on Ronald Reagan and his administration, was also a referendum on a very independent and very separate Republican majority in the Senate."

Baker went on to say, "It is really, I think, the most satisfying thing in my political career to be able to infer from the result tonight that the country perceives and understands that the Republican majority in the Senate is an independent political force, and that we have performed in a way that they approve. Now, that's not going to be changed in the next two years."

Baker expressed the hope that the added sharing of responsibility placed on both Republicans and Democrats alike would not break down into two years of confrontation.

"I hope we don't make political football over great issues that we've got to solve in the next two years," he said. "Social Security comes to mind. Defense spending and tax policy, of course, come to mind . . . . One thing we mustn't permit to happen is for the two bodies to be in conflict to the point where we immoblize the functions of the Congress."

Two other GOP leaders, also speaking before national TV audiences, underscored his points.

House Minority Leader Robert H. Michel (R), speaking on ABC's Good Morning America after winning his extremely close race in Illinois, acknowledged that there will have to changes -- "adjustments," he called them -- in the president's approach. "Maybe we've got to have a more pragmatic type of coalition," he said.

Michel also warned against confrontation and stalemate. "We've got to make it work," he said.

Michel, Baker, and Sen. Robert J. Dole (R-Kan.), another GOP leader who will play a major role in the next session of Congress, agreed that the economy overshadows every other election issue and requires urgent attention. As Michel said, "we must speed up the recovery. It's got to come pretty quickly."

Dole, speaking in an NBC interview, focused the task facing Reagan and the Republicans by saying: "If we can't address the economy first, we may not be around to address the social issues."

Behind all these words seems to lie a recognition among key members of both parties that the voters want them to work together in a different political arrangement, and that any previous determination to stick too rigidly to a specific course must be reassessed.

The final question is whether Ronald Reagan reads the returns the same way.