President Reagan hadn't even reached the White House in his inaugural parade yesterday before running into trouble with a leader of the right wing of his own party in Congress.

Puncturing the euphoria of the day for Republicans, Sen. Jesse Helms (R-N.C.) took the floor of the Senate to oppose confirmation of one of the new president's principal Cabinet choices, Caspar W. Weinberger for secretary of defense.

Weinberge was eventually confirmed by a vote of 97 to 2 -- the first of more than a dozen Cabinet nominees who are expected to be confirmed in almost assembly-line fashion by the newly Republican-controlled Senate over the next day or two.Voting with Helms against Weinberger was Helms' new Republican colleague from North Carolina, John P. East.

None of the nominees is seen to be in trouble, with the possible exception of Raymond Donovan, Reagan's choice for secretary of labor, whose confirmation has been held up pending investigation of charges that he made payoffs to secure labor peace for his construction firm. Secretary of State-designate Alexander M. Haig is in line for confirmation today.

As his first official act after being sworn in as president, Reagan signed the nominations of 17 Cabinet and other top administration officials at a cermony attended by congressional leaders in the small, ornate President's Room off the Senate floor. Reagan was barely out of the Capitol when the Senate took up the nominations and Helms took the opportunity to, as he put it, "draw the line, a benchmark as it were, to measure the progress of the reconstruction of our national strength."

Claiming to speak for a "great number" of his silent colleagues who plan to go along with Weinberger's confirmation, the arch-conservative North Carolinian launched into a lengthy critique of Weinberger and "his handpicked deputy," Frank Carlucci, a veteran bureaucrat and the current deputy director of central intelligence, whom Reagan has nominated as deputy secretary of defense.

Vowing to oppose Carlucci's confirmation as well, Helms charged that Weinberger is "not at this moment prepared to make the clean break with the very policies of the past which have managed our military and international decline" -- and said that Carlucci's "talents reinforce Mr. Weinberger's weaknesses and obviate his strengths."

With Democrats looking on with amusement as Reagan's first congressional knuckle-rapping came from his own right wing, Helms praised Weinberger's record as a budget-cutter but said this wasn't sufficient for the nation's defense chief. "The national crisis which America faces is a crisis of sheer survivial," said Helms, "and for survival, Mr. Weinberger's dedication to efficiency, frugality and sound management simply are not enough."

He said Weinberger lacks "resolution" and "vision" in dealing with the Soviet Union and displayed "astonishing naivete" in his outlook on strategic arms negotiations with the Russians during his confirmation hearings, which Helms called a "dismaying performance." He also criticized Weinberger for dismissing a transition team of defense hardliners and "consign[ing] their reports to oblivion."

No other senator spoke out against Weinberger. But several, including conservative Sen. Strom Thurmond (R-S.C.) and assistant Democratic leader Alan Cranston of California praised his previous roles as budget director and secretary of health, education and welfare in the Nixon administration. "He will see that we have a strong defense," said Foreign Relations Committee Chairman Charles H. Percy (R-Ill.).

The Democrats settled quietly, if not entirely comfortably, into their new role of Senate minority, although Sen. William Proxmire (D-Wis.) forced a roll-call vote on each nomination and promised pointed questions about most of the nominees, complaining of atrophy in the Senate's historic role of advice and consent on Cabinet nominations. Proxmire complained that some nominees resembled "prisoners of war trying to keep vital secrets from the enemy" during their confirmation hearings.

Apart from the Senate skirmish over the Cabinet, the corridors of Capitol Hill were overflowing yesterday with food, drink, skipping children and constituent festivities. There were large gatherings such as the sumptuous open-bar gala for hundreds that Pennsylvania Republican Rep. Richard T. Schulze threw in the gold-carpeted room of the House Ways and Means Committee. And there were little get-togethers like that of Rep. Ronald E. Paul, a second-term Texas Republican, who had chili, cold cuts and conversation in shirtsleeves for anyone who happened by.

"Everybody's real optimistic that Reagan is going to turn off the spigot of government," said Paul, who boasts of voting against every spending bill. "But I'm less optimistic. The momentum of big government is so strong that even good intentions and big words are not going to be enough. Turning off the spigot is much more difficult than people realize."

While New Jersey Republican Rep. Millicent Fenwick served dainty pastries and Texas Democrat James Mattox served coffee from a silver urn, many members, such as freshman Lynn Martin (R-Iowa), were out watching the parade. And several congressmen's quarters were locked. At the office of Rep. Clay Shaw (R-Fla.), on of his constitutents, a university president, had stuck a forlorn business card in the crack of the door.