Jostled from the left and right, scorned by the true believers, targeted for extinction by the militants, they are the battered stepchildren of the Republican revolution in the United States Senate.

Then why are so many of these moderate-to-liberal Senate Republicans -- the quintessential minority on Capitol Hill -- smiling these days while conservatives like Jesse Helms (R.-(N.C.) are firing loud warning shots across the bow of the Reagan administration ship?

One reason is basic Senate arithmetic. With 53 Republicans, 46 Democrats and one independent, any group of a dozen or more senators can wind up holding the balance of power in a close partisan or ideological split.

"No Republican measures can be passed without the support of this group," says John H. Chafee (R-R.I.) of the moderate-to-liberal wing. On issues ranging from civil rights to foreign aid, "we can play a very significant role," says Charles McC. Mathias (R-Md.).

Even though Republicans can usually count on a significant number of votes from conservative-leaning Democrats, who are also in a balance-of-power position and are now beginning to caucus among themselves to wield greater power, the GOP could face loss of its narrow new majority on critical issues if too many of its own members jump ship.

It is the reverse mirror image of the problem faced by the Democratic majority in the House, where there are enough conservative Democratic shipjumpers on economic, national security and other issues to tilt this last bastion of the Democratic Party in Washington rather heavily to the right.

But the euphoria of many Republican moderates stems from more than projected body-counts in future legislative wars. No matter that some battle-scarred veterans of Republican infighting decline to share in the ruffles-and-flourishes optimism, fearing, among other things, that the mood in both parties has swung so far to the right that left-leaning Republicans and right-leaning Democrats may simply cancel each other out.

Simply put, many GOP moderates appear happier with the early outlines of the Reagan administration, including appointments, than some of their conservative counterparts do. And especially those who consider themselves fiscal conservatives but social liberals, as many do, believe that President Reagan's economic program is moving their way with such a strong political imperative behind it that divisive issues like abortion, prayer in schools and retrenchment on civil rights will be driven off the legislative agenda for months if not years.

To an extent, at least, some conservatives agree. "Moderates have less complaints than they ought to have," complained Paul Weyrich, director of the New Right's Committee for the Survival of a Free Congress.

"I'm very upbeat," said Chafee, a soft-spoken New England moderate who sees in Reagan a fellow "pragmatist." He went on: "I don't think you're going to find a schism. We're so united on our concern about the economy that other issues are going to be put aside."

"Before the election, I had the strong feeling we were the people that Ronald Reagan really needed to make things work, and I still feel that way," commented David Durenberger (R-Minn.).

"Isn't it interesting," asked Mark O. Hatfield (R-Ore.), smiling broadly at the thought, "that the first one to break from the traces was Jesse Helms and not one of us?"

Hatfield's observation came only a couple of days after Helms spoke out against confirmation of Caspar W. Weinberger as secretary of defense, questioning his credentials as a hardliner, and put a hold on confirmation of Weinberger's designated deputy, Frank Carlucci, for basically the same reason. Helms also hoisted warning flags about some reported choices for top-level jobs in Alexander M. Haig Jr.'s State Department.

By way of contrast, Hatfield, a long-standing critic of Pentagon excesses, had only good things to say about Weinberger. "Weinberger has assured me that the magnifying glass will be put on military expenditures as it will be on social programs," said Hatfield, who has just taken over as chairman of the Senate Appropriations Committee. "We're presented with the greatest opportunity we've had in a long time to get at cost factors that don't affect our national security -- that even detract from it because they waste money."

Many of the Republican liberals and moderates were not early supporters of Reagans's conservative-backed drive for the presidency, but they say now that they expect to be with him long after some of the ideological purists have bailed out.

"I give President Reagan about six months before the right wing is nipping at his heels or worse," said Bob Packwood (R-Ore.), although he emphasized a belief that, because of the importance of consensus on economic issues, there will be little to divide Republicans within the Senate over the next couple of years.

But all is not brotherly love between the ideological fringes of Senate Republicans. Nor is the heady optimism of many moderates shared by all left-of-center Republicans, whose ranks have been riddled in recent years by conservative coups that ended the careers of such liberal stalwarts as Clifford Case (N.J.) and Jacob K. Javits (N.Y.).

Mathias, for instance, has been put in his place for a second time by oldguard conservative Strom Thurmond (R-S.C.), who blocked Mathias' ascension as ranking minority member of the Judiciary Committee in 1976 by giving up his ranking position on Armed Services to pull rank on Mathias on Judiciary. When Thurmond became chairman of Judiciary in the Republican takeover of the Senate this year, he and his committee allies abolished the antitrust subcommittee that Mathias was in line to head and curtailed the jursidiction of the criminal justice subcommittee that Mathias wound up with. Thurmond, commanding enough votes on the committee to prevent a Mathias counterattack, transferred responsibility for the Federal Bureau of Investigation and Drug Enforcement Administration from Mathias' subcommittee to a new subcommittee headed by fellow conservative Jeremiah Denton (R-Ala.).

Mathias, for his part, has given speeches from New York to California warning of "disturbing signs on Capitol Hill . . . that the election results have been taken as a license to declare open season on our civil liberties." Regarding Thurmond, Mathias goes on to ask, "What does it portend for civil liberties when the chairman of the Senate Judiciary Committee favors repealing the Voting Rights Act?"

Mathias, one of the most liberal Republicans, voices general if somewhat qualified praise for the way the Reagan administration has launched itself, saying the president's appointments are "in the mainstream of American political thought" and "will mean that when changes occur, they will not occur in a precipitous or radical way."

But he does not claim there will be no bumps on the road. If there are some, he foresees Republican liberals and moderates staving off assaults on the Voting Rights Act and helping prevent, among other things, a return to presidential impoundment of congressional appropriations, a severe cutback of foreign aid to Third World countries, drastic changes in labor laws and any major relaxation of environmental safeguards.

Mathias notes pointedly that "60 is the magic number in the Senate," a reference to the number of votes needed to head off filibusters or other delaying tactics, which used to be employed by conservatives in the days when liberals ran the show on Capitol Hill and could well be used by embattled liberals in the future.

Similarly, Packwood contends that Republican moderates, in combination with many Democrats, can thwart the two-thirds vote that would be required to send to the states a constitutional amendment banning abortions, which conservatives are pushing.

But Lowell P. Weicker Jr. (R-Conn.) is not optimistic about any swing-vote role for Republican moderates, largely because, he says, "You can't look to the Democratic Party anymore as playing a lead role in civil rights and civil liberties." In all, says Weicker, the conservatives' ideological edge in the Senate is far greater than the 53-to-46 party line split would indicate.