hen Sen. Orrin G. Hatch (R-Utah) came before congressional budget conferees in Washington a few months ago to appeal for more money for some social welfare programs, Rep. Stephen J. Solarz (D-N.Y.) exclaimed in mock amazement, "If I didn't know better, I'd have thought I just heard the distinct accents of a born-again liberal."

Solarz did know better. But Hatch, who came to the Senate five years ago as a bright young legislative guerrilla fighter from the New Right, is now ensconced in the Senate power structure at the head of one of its most important, politically sensitive and delicately balanced committees: Labor and Human Resources.

Both in Washington and back home in Utah this summer, the strain is showing.

Wearing his committee chairman's hat, Hatch has made--or at least acquiesced to--some compromises that anger the true believers on the right. His agreement in a budget conference to keep the federal family planning program has provoked an outcry, and he's taken "a lot of hell" for supporting Sandra D. O'Connor's nomination to the Supreme Court. "Although his record is conservative," said Paul M. Weyrich, head of the New Right's Committee for the Survival of a Free Congress, "we can never be sure where the hell he is."

On the other hand, Democrats contend Hatch has positioned himself so far from the political center that a popular moderate Democrat like Gov. Scott M. Matheson or former governor Calvin L. Rampton, if one of them could only be convinced to run, could mount a formidable campaign against Hatch when he comes up for reelection next year. His appeal is too far to the right, says State Democratic Chairman Mike Miller, contending that conservative Sen. Jake Garn (R-Utah), who won reelection handily last year, has done a much more effective job of reaching into the political center.

But right now the Democrats' chances don't look too good, and Hatch's right-wing critics are unlikely to move against him.

Moreover, Utah is bedrock Reagan country and Hatch benefits from long and close association with the president.

Still, Hatch, campaigning almost frenetically during a recent visit to the state, seems to sense his own vulnerability, just as he did in Washington shortly before in insisting that the White House "share the responsibility," as Hatch put it, for any painful concessions that Hatch had to make as a conferee on President Reagan's spending cuts.

In Utah, Hatch, Pennsylvania-born but with roots that extend deep back into Utah's Mormon past, appears most nettled by charges that he's an outsider, a campaign that has already spawned a bumper sticker reading, "Send Hatch Back Home to Pittsburgh."

Hatch responds by passing out "I Love Utah" buttons (20,000 so far) and tromping around in what he calls his "Sagebrush Rebellion boots." He acknowledges that he's never found a pair that fits but tells Utahns proudly, "They drive 'em nuts back in Washington."

As for the Pittsburgh connection, he notes that his family's roots in Utah go all the way back to "a couple of Mormon polygamists so there are Hatches all over Utah."

Hatch's sensitivity extends to legislation as well. When a woman who is working for sex equity in vocational education programs stopped by his office, Hatch greeted her warmly and lamented, "I'm the guy who gets the blame for shutting the programs down, but I'm the one who saved a lot of them."

Similarly, he visited a Job Corps center at Clearfield, north of Salt Lake City, calling attention to the fact that he helped save the program, which he identifies as one of the government's more successful job-training efforts, from even more severe cuts than it received.

"He's always looking over his shoulder at his image, and it keeps getting in his way," said a Republican colleague in Congress, not unsympathetically. "He keeps tripping over his own insecurities," commented a GOP staff aide.

The irony is that Hatch, fresh-faced and clean-cut and even more youthful appearing than his 47 years would indicate, is such an adept debater and public speaker that he projects the image of brash confidence--a quality that contributed to his reputation in conservative circles as a giant killer when it comes to liberal legislative initiatives.

With a tenacity that is shared by few of his colleagues, he triumphed in a filibuster against President Carter's big package of labor law changes in 1978 and more recently in a rear-guard action against Senate Democrats' swan-song effort to strengthen fair housing legislation late last year.

But the job of running the Labor and Human Resources Committee (he once called it "the pits" in a conversation with reporters in Utah) makes the lonely filibuster vigils look like a legislative frolic.

The committee has jurisdiction over major health, welfare, education and employment programs and has always been a stronghold of liberals. As Hatch noted when he made his case for a budget-expanding compromise before the conferees' panel, "I chair a committee that I don't think has ever made a cut in its existence."

A storm center of the budget cuts, the committee has an equal number of liberal Democrats and conservative Republicans, with two Republicans of more liberal persuasion, Sens. Lowell P. Weicker Jr. (Conn.) and Robert T. Stafford (Vt.), holding the balance of power.

The result has been compromise, less than totally satisfactory to the administration, on such important issues as consolidation of many federal programs into block grants to the states, a policy change that Hatch strongly favors.

Probably no senator was in a less comfortable position than Hatch as the final budget compromises were worked out, and some colleagues complained privately that his agonies were spread around the table for all to share. At times, patience wore thin. According to one observer, when Hatch complained at one point that he didn't have the same kind of private hide-away in the Capitol that his colleagues did, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) impatiently told Hatch to take his office if he wanted one that badly.

But Hatch claims that the final result was "much better than it could have been." As for the committee, he says, "We're winning by attrition, but you can't convince all the conservatives of that." He quoted a Democrat as saying, "We like you but you never quit."

Hatch moves about Utah with much the same intensity that he does in Washington, gleaning political lessons from even chance encounters. After a radio interview that threatened never to end, Hatch bounced to life when the proprietor told him he would gladly hire one or more young minority workers if he didn't have to worry about running afoul of federal regulations--which is a message that Hatch has been sending for some time.

A trial lawyer before entering the 1976 Senate race as a political unknown, Hatch always seems to be arguing a case, and even his critics say he does so with great skill. He seems to unbend only with some effort, going out of his way to convince companions that his reputation for humorlessness is unfounded. Earnestness is his trademark.

Like Reagan but unlike most of his conservative Senate colleagues, Hatch can legitimately claim a labor and liberal Democratic background. In Pittsburgh, he grew up a Democrat and worked in the unionized building trades before becoming a labor lawyer. In 1969, he and his wife moved to Utah to raise their six children, he explains, adding that he left the Democratic Party even before leaving the East. He continued practicing law with no overt political ambitions until 1976, when he plunged into the race for the Republican nomination to oppose three-term Sen. Frank Moss (D-Utah).

With a timely assist from Reagan, he won the nomination over well-established opponents and went on to topple the liberal Moss in November.

In Utah as in Washington, his dominant theme is free enterprise conservatism, with heavy punches at the opposition, levened by an almost inevitable claim of affection for the personalities involved--from House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and Sen. Edward M. Kennedy (D-Mass.) to AFL-CIO President Lane Kirkland and National Organization for Women (NOW) President Eleanor Smeal. He likes them all but savages their politics. "What's compassionate about putting our freedoms in jeopardy . . . by spending this country into bankruptcy so politicians can buy a few votes?" he asks when the compassion of Republican economic policies is questioned.

Hatch's approach draws applause from supporters--and rage from foes. "He campaigns against 'big labor bosses', but he's the first to put his arm around me and say that if all union leaders were like me, we'd have no problem," complains Utah AFL-CIO President Ed Mayne. It's vintage Hatch and, Mayne's indignation aside, it seems to be good politics, so far