With the outlook dim that the House will approve President Reagan's $36.3 million contra aid request today, many members of Congress fault Secretary of State George P. Shultz for failing to use his prestige on Capitol Hill more effectively over the past six months on behalf of the contras.

State Department spokesman Charles E. Redman, calling such criticism "so absurd that it almost is not worth answering," said Shultz in the past two weeks has met with undecided members of Congress and groups that could influence the vote, made "innumerable phone calls" and will lobby Capitol Hill "right up to the end." Shultz testified at length yesterday before the House Foreign Affairs Committee in a last-minute bid for contra aid.

Despite these efforts, many House members and senators, including some from Shultz's own Republican Party, expressed surprise at what one called "the sporadic, on-again, off-again nature" of Shultz's involvement in the congressional debate.

They maintain that Shultz's disengagement further damages the administration's case because it puts the principal responsibility in the State Department for Central America on Elliott Abrams, assistant secretary for inter-American affairs, who is persona non grata to House Speaker Jim Wright (D-Tex.) and other key Democrats, who have not forgiven him for making misleading statements to Congress about past secret funding of the contras. The Democrats also suspect that Abrams' outspoken anti-Sandinista stance makes him hostile to the Central American peace process.

The result has been an almost unprecedented breakdown in communication between the administration and Congress over a major policy issue. The Democrats refuse to deal with Abrams and discount Reagan's statements about contra aid.

Many lawmakers say that while they do not doubt Shultz's sincerity in pleading for contra aid, they have the impression that his mind is on other matters.

"It may be that his attention was diverted by other things such as the arms control negotiations with the Soviets and the summit meeting with {Soviet leader Mikhail} Gorbachev," said Sen. John S. McCain III (R-Ariz.), a contra aid supporter.

Many Democrats feel that Shultz's greatest missed opportunity was last summer when he let the administration distance itself from a collaboration with Wright that Democrats saw as the only chance to forge a bipartisan consensus on Central America and the contras.

They say Shultz weathered the Iran-contra scandal as the only senior Reagan administration official whose judgment on such ideologically heated issues as Central America policy is respected by Democratic congressional leaders. Shultz enhanced this image last August when he joined Wright on Reagan's behalf to work out a joint regional peace initiative.

But when Nicaragua and four of its neighbors signed a peace agreement proposed by Costa Rican President Oscar Arias last Aug. 7, Shultz, in the view of influential Democrats, was displaced by administration conservatives who want to continue the U.S.-backed contra insurgency against the Sandinista government even if it scuttles the peace process.

Wright felt the administration had abrogated his understandings with Shultz, who in turn resented Wright's later forays into diplomacy as infringing on the president's power to conduct foreign policy.

A Wright aide summarized the speaker's views this way: "Shultz saw he would have to battle the most right-wing elements in the administration and Republican Party at the same time he was facing a similar fight with the same people over arms control. He apparently said to himself, 'I can take on one of these fights but not both,' and he opted to give priority to arms control. But . . . he surrendered control over Central America policy to the hard-liners."

McCain, though on the other side, seemed to agree. He said that during a White House meeting on the aid package last week, Shultz spoke briefly but took no part in the heated discussion that followed, leaving Abrams' as "the strongest voice," McCain said.

Said McCain of Shultz: "I have the impression that he is a man who enjoys talking to {Soviet Foreign Minister Eduard} Shevardnadze."