A little-noticed vote by a House subcommittee on trade last week could spell new trouble between President Carter and Congress and give encouragement to protectionist forces in industry.

By 7 to 6 the Ways and Means subcommittee on international trade, chaired by Rep. Charles A. Vanik (D-Ohio), voted to grant U.S. makers of industrial fasteners - nuts and bolts - high protective tariffs that Carter had ruled against on Feb. 10.

The nuts and bolts, imported mostly from Japan, are widely used in the automotive and other industries.

If confirmed by the committee and both houses of Congress, tariff relief for the industry would not only be a personal rebuff to the President but also might encourage further protectionist challenges to his generally open trade stance, officials fear.

"The President felt this was a poor case for granting relief," White House aide Stuart E. Eizenstat said after the vote. "The cost would have been about $200,000 per job saved for the domestic industry. It would have been inflationary and economically unjustifiable, even though politically it would have been easier to go the other way."

The subcommittee decision reversing Carter will soon come up before the full Ways and Means Committee. The committee hasn't voted on a trade issue so far this session, and no one on Capitol Hill is willing to predict the outcome. Eizenstat said he is "hopeful" but "not confident" that the full committee will support the President.

Committee chairman Al Ullman (D-Ore.) told The Washington Post he would not support the Vanik subcommittee decisions, but had no prediction on the ultimate result. Administration sources fear that if the issue goes to a floor vote in either house, it could have wide political appeal and be difficult for Congress to reject.

U.S. nuts and bolts makers originally sought protection against $230 million of imports in hearings last year before the U.S. International Trade Commission. On Dec. 7, the ITC recommended steep increases in tariffs for periods up to five years on the iron and steel nuts, bolts and screws used by the auto and many other industries.

Carter got divided recommendations from his advisers on how to deal with the ITC decision. The State Department, Treasury Department, and Council of Economic Advisers adversed him to reject it. They counseled that the domestic industry had not been injured by imports, and that the tariff scale recommended by the ITC would be highly inflationary.

On the other hand, the Office of the Special Trade Representative, and the departments of Labor and Commerce urged Carter to go along with some relief for the industry. A collateral argument made on the industry's behalf is that it needs protection so it can maintain a flow of supplies in time of war.

The fact that Special Trade Representative Robert S. Strauss - Carter's key adviser on such issues - was on the side of the some help for the industry led to the general belief among its supporters in Congress that Carter would approve the basic thrust of the ITC decision, perhaps with some modifications.

But Carter sided with his free-trade advisers, and rejected it. "I was stunned by the reversal," Vanik said in a telephone interview.

Vanik, who supports the industry's argument that without protection afforded by higher tariffs about 2,500 out of 13,000 jobs would be wiped out, led a revolt in his subcommittee.

Under the Trade Act of 1974, a presidential decision to bar relief under the escape clause provisions can be overturned by Congress. Despite what Vanik described as hard work by the White House "that converted two or three members who really believe the President was wrong." Vanik got his 7-to-6 vote to overturn on Tuesday with the help of two Republicans, William Steiger of Wisconsin and Guy Vander Jagt of Michigan.

Administration lobbyists - including Strauss' office, which originally favored relief for the industry - now see the issue as more significant than the narrow question of protection for the fasteners industry.

"The president shouldn't be overridden unless his actions have been capricious, not merely where there has been a different of opinion," one administration aide said. He cited the approximately equal division among the Carter team and in the subcommittee itself as evidence that "the decision is one of those that could have gone either way."

What the White House clearly fears is that support of the Vanik subcommittee would not only to be taken as new encouragement to protectionists but also as a personal rebuff to Carter.

Vanik rejects this line of reasoning."They could have avoided the whole issue," he said, "but they chose to take it on." The Ohio congressman said that Carter could have come up with a compromise that would have satisfied the industry.

"This has got nothing to do with the president's popularity nor is it a tarnishment of his trade policy," Vanik said. "The nuts and bolts affair doesn't have worldwide implications, but [our vote] does tell workers and industry that the trade act is working the way it's supposed to."

Reinforcing Vanik's criticism of the administration's stance is a frustration he says he and other members feel over general economic policy. For example, he said in a formal statement earlier last week that he was "shocked" that Congress was not told before its original consideration of the debt ceiling two weeks ago that there was a new "shortfall" of $8.8 billion in the estimated fiscal 1978 deficit.

Vanik also complained that Treasury Secretary W. Michael Blumenthal did a fast reverse on the question of offsetting Social Security taxes by agreeing, first, that the matter should be looked into this year, then saying no action should be taken.

"They haven't got their act together," Vanik said. "Now they complain we're challenging their judgement [on nuts and bolts]. Well, I'm not so sure how good their judgement is."