President Carter today will resume his sometimes contradictory courtships of two groups whose important support eluded him last year - the business community and the Democratic Congress.

Carter will deliver his State of the Union address to a joint session of the recovening House and Senate at 9 p.m. A principal topic will be the economy. In this basic address, in the special economic and anti-inflation message he will sent to Congress on Friday, in the tax cut plan he will announce Saturday and in the budget he will submit next Monday - Carter will essentially be asking all sides to content themselves with an unspectacular economic policy stuck in the middle of the road.

His course will represent an attempt to resolve the basic economic dilemma facing him and the country: to finally pull the nation out of the long recession of the 1970s, the economy must continue to grow, and businesses must be persuaded to invest in new plant and equipment. But if this growth is accompanied by reintensified inflation, that will deprive the consuming public of real new buying power, and business may not feel an incentive to modenize and expand productive facilities.

Part of Carter's response to this dilemma will be a plea for patience from those Democratic members of Congress who want to spend more federal money for aid to cities, welfare and health care reform and other social and public works programs. At the same time he will chart a cautious, middle-of-the-road economic program including large tax cuts meant to cal mand encourage private enterprise.

But tonight's State of the Union message will go well beyond economic policy. Carter is expected to restate his support for a long list of measures proposed last year, from his energy program to the Panama Canal treaties to welfare reform and more.

Though Carter has publicly acknowledged tht he may have tried to do too much last year, and Vice President Mondale has been assigned to set priorities and plan a Schedule for the administration's legislative program, the impression persists on Capitol Hill that Carter is still asking for too much.

After meeting with Carter yesterday, Sen. William Proxmire (D-Wis.), chairman of the Senate Banking Committee, told reporters he doubted the President could get tax revision through Congress this year because "we have so much else to do this year."

Proxmire added, however, that Carter has "every chance of getting a very simple tax reduction bill through."

Administration officials acknowledge privately that Proxmire's view may prevail in Congress this year.

Reservations about tax revision are symptomatic of a general mood of caution and independence that seems to prevail on Capitol Hill, Carter has few ardent supporters in either house, and few members of either body seem to perceive political pressure from their constituents to support the President's program.

On the other hand, majorities in the House and Senate share the President's program.

On the other hand, majorities in the House and Senate share the President's broad economic goals, and as Proxmire suggested, there is widespread eagerness to cut taxes for both political and economic reasons.

Many members of Congress have returned to Washington after the long Christmas recess with a strong sense of the electorate's uneasiness about what is going on in Washington.

"Basically, the feeling is one of still some uncertainty and apprehension," according to Rep. Elliott H. Levitas (D-Ga.), whose Atlanta constituency includes Jimmy Carter's old backyard.

Levitas said many of his constituents were disappointed that Carter has seemed to depart from the concerns that "they feel were responsible for his election," such as a balanced budget, reformed bureaucracy and better-managed government.

Levitas was one of the sophomore congressmen who met Tuesday with Carter and other senior administration officials, and he said afterward he was disappointed in what he heard. The effort by Vice President Mondale to attach priorities to various administration proposals "did not succeed," Levitas said. "They've run out the old laundry list again."

At the top of the list is the energy legislation that Carter continues to call his top priority. But the President may have less support than ever for this energy program after this congressional recess.

Last year Sen. Russell B. Long (D-La.) predicted privately that the Congress would find it much harder to vote the large energy taxes that Carter calls the heart of his program after voting for huge new Social Security taxes.

Long sought briefly to delay action on Social Security tax increases in hopes of getting a vote first on energy taxes, but his ploy didn't work.

Now, numerous members of Congress report that their constituents expressed strong resentment at the new Social Security taxes during their visits home over the holidays. Rep. Samuel S. Stratton (D-N.Y.) said that for his upstate New York constituents, "the economy and certainly the Social Security thing were probably the major areas of complaint."

Rep. Sidney Yates (D-Ill.) mentioned Social Security taxes first among the subjects raised by his constituents over the holidays.

Whether the administration can still get both House and Senate to approve big new energy taxes remains highly problematical, according to many congressional sources.

If the energy bill fails - or is substantially watered down before enactment - this would be consistent with the fate of all the administration's relatively bold initiatives. On all of them so far, the 95th Congress has opted for more modest action (or no action at all).

Carter will offer more initiatives this year - modest tax revision, welfare overhaul, civil service changes, and perhaps others. He will also continue to press for some of the ideas the Congress declined to deal with last year, such as hospital cost containment.

Congress will have another agenda to deal with, including about 90 authorization laws that exprire during the coming year, and the major portions of Carter's economic package, particularly tax changes and the budget.

There will also be time-consuming debates in the Senate on the Panama Canal treaties, and on an arms limitation agreement if one is reached and the administration decides to submit it to the Senate in an election year.

If Carter is unable to assume a strong position of leadership in his dealings with Congress, the possibility remains that the business community will continue to look at his administration askance, and continue to withhold the investment capital so necessary to create the economic growth that Carter must have to pursue his goals.