A few years ago, they started rolling in from the right the Senate floor like so many of loose tumbleweed off the deserts, plateaus and rangelands of the mountains West.

As an exotic variant of the old conservative Republican stock, they drew little more than curiosity and occasional outbursts of impatience and derision from the comfortable, secure Democratic majority.

Even older conservatives -- to say nothing of more moderate Republicans -- kept their distance as the often brash newcomers pursued confrontation, media attention and a host of social causes typified by the fight against abortions, especially federal financing of abortions for the poor.

But next year this minority within a minority, joined ideological brethren from east of the Continental Divide -- in fact from every region of the country -- will have the votes to command a majority on most issues in the Senate.

The 1980 elections not only ended a quarter-century of Democratic domination of the Senate, but also roughly doubled the ranks of these new-breed conservatives.

The elections catapulted some of them -- James A. McClure of Idaho, Jake Garn and Orrin G. Hatch, both of Utah, and Jesse Helms of North Carolina -- into important committee chairmanships.

Perhaps their most widely respected leader, Sen. Paul Laxalt of Nevada, will be president-elect Ronald Reagan's point man, a position of independent influence rivlaing that of Sen. Howard H. Baker Jr. (R-Tenn.), who is in line to become the elected majority leader.

In the House where the Democrats retain control with a shruken 26-vote margin, the new-era conservatives also are on the rise, joining with older conservatives and right-leaning Democrats to form a bipartisan right-of-center coalition that is expected to be the dominant force in the body during the 97th Congress.

Together, their common bond is more of style than substance, although the differences are far from merely cosmetic.

On many critical issues, such as more spending for defense and less for New Deal-Great Society social programs, on an almost religious preference for the private sector over the public sector, the old and new conservatives generally vote alike.

But the younger conservatives (some accept the New Right label, while others reject it as too narrow) are generally more activist, experimental and confrontational -- a contrast that often makes them appear even more right wing than their forbearer, although the reverse may also be true.

Malcolm Wallop (R-Wyo.), a tall, rangy, 47-year-old cattle rancher with a degree in English literature from Yale, puts it this way:

"We emerged in an era where we began to tailor program to the philosophies we were expressing. The older conservatives were there primarily as resisters to the liberal wave that started in the '30s. Theirs was essentially a defensive battle. Ours is an offensive battle, where we have complaints about the direction that the country is going, but also positive alternatives to offer.

"Instead os moaning about the welfare state, [we're] aiming for funding mechanisms other than government to accomplish essentially the same goals -- to lead the country through incentives rather than direct the country by fiat."

According to Paul Weyrich, director of the Committee for the Survival of a Free Congress (CSFC), one of the network of outside organizations that the whole New Right movement has spawned, there are other distinctions as well.

One is a lack of paranoia about the oposition.

"Now it's the left that's coming up with all these charts and graphs about who's on who's board of directors," Weyrich observed with obvious relish. "If the liberals continue on in this way, it will take them as long to get back as it did the conservatives."

Another is openness with the press.

"They know who they are, they're proud of it, they figure they have nothing to hide," he added.

The new conservatives often are more accessible to reporters than liberals, to say nothing of some older conservatives who tended to view the press as an enemy plot. Moreover, some, like Helms, came out of radio, television and newspapers and understand media manipulation.

They're also strong on coalition-style organizatin to accomplish their objectives -- a strategy borrowed from liberals but used more effectively in recent years by conservatives to oppose measures ranging from a package of labor law revisions to the SALT II treaty with the Soviet Union.

They have had their own organization within the Senate, called the Steering Committee, which includes other conservatives but is dominated by the newer breed. There also is an organization of staffers, along with networks of contacts to sympathetic House members and to outside groups such as Weyrich's CSFC and the Heritage Foundation, a relatively new think tank for the right.

Finally, their range of interests is broader than that of their elders, dipping into such politically emotional issues as abortion, school busing for racial reasons, prayer in schools, the Equal Rights Amendment and a whole raft of sensitive "pro-family" issues. Few of these issues may command huge constituencies, but they can mobilize enough people to make a difference in a close election.

Even in the Senate, where the new conservatives are most identifiable as a group, it is not easy to pin down their precise count or catechism because many are as strong on individuality as they are on ideology.

Helms pushes hard on abortion; Wallop doesn't. Sen. Richard Lugar (R-Ind.) joins, even leads, the pack on some issues but is not counted by insiders as part of it. Sen. Alan K. Simpson (R-Wyo.) is too much of a maverick. Sens. Strom Thurmond (R-S.C.) and Barry Goldwater (R-Ariz.) normally vote with the younger conservatives on their issues but are, in the words of one of them, "old school." Said an aide to one of the newer senators: Barry is venerated more than followed."

Adding to the complexity is that fact that some, even more than just a few, are sending out uncharacteristic new signals of caution, moderation and consensus-seeking now that power has been thrust upon them.

Take McClure, for instance.

The soon-to-be chairman of the Senate Energy Committee yields to few in his sagerbrush-brand of conservatism or his enthusiasm over the gains of his group. But he's also examined the voting results from the November elections and points out that 11 of the 22 Republican senatorial victors won by 52 percent of the vote or less.

"It was broader than it was deep," said McClure, speaking in a recent interview of the 1980 republican sweep. "It doesn't mean a blanket endorsement of all we stand for . . . . It makes us more cautious than we would otherwise be."

On policy issues, McClure has warned not to expect a wholesale dismantling of Democratic-inspired energy or environmental programs, although, predictably, he will seek a greater emphasis on the private sector. As for the "sagebrush rebellion," expectations that Reagan will loosen the hand of the government in managing federal land in the West "may well take the steam out of the rebellion," says McClure.

A newer member of the group, Sen. William L. Armstrong (R-Colo.), talks earnestly about "pursuing the peaceful overthrow of government" with "confrontation politics" but at the same time wants to see "the Republican Party broaden its base . . . to reach out and make new friends." He applauds Reagan's postelection gesture of accommodation to District of Columbia Mayor Marion Barry and has doubts about a proposal from his colleague Hatch for a constitutional amendment to curtail affirmative action programs for minorities and women.

"Most of us will temper our impulses toward excess because we believe that what we're doing is so important," Armstrong said in an interview.

For his part, Hatch, who will be chairman of the Senate Labor and Human Resources Committee in the new Congress, is putting out conciliatory signals to unions and actively soliciting alternative proposals for some of his pet projects, such as lower minimum wage for teen-agers.

According to those who watch them most closely, the hard core of this emerging power center in the Senate probably numbered no more than eight or 10 in the Congress that is coming to an end this week, although many more old and new conservatives, occasionally including Democrats, could be counted on for support depending on the issue.

Most of the 15 new Republican senators, as many as 10 to 12 of them, are being counted as likely recruits in the new Congress. Some, such as Sen.-elect John P. East, a protege of Helms, are regarded as more conservative than most of the earlier group.

"I think East may make Jesse look like a liberal," chuckled one of Helms' colleagues the other day.

Helms figures that the philosophic shift in the Senate is far greater than the numbers (from 59 to 41 in favor of the Democrats to 53 to 47 in favor of the Republicans) would indicate.

"Most like 60-4- conservative instead of 60-40 liberal-to-moderate," he said the other day. "There are a lot of closet conservatives over there on the Democratic side who won't be having a president or a committee chairman or a majority leader putting pressure on them now."

Frank Madsen, administrative assistant to Hatch, has talked to a number of the newly elected conservative senators and believes they will be less ideological than their campaign rhetoric would indicate. But many of them will be coming to Washington without the leavening of legislative experience and the lessons it teaches in influence through compromise.

The effect these newcomers will have on the Senate and the Republican majority cannot be known until they settle in after Jan. 3. There appears to be ample opportunity for dissension in the ranks, if for no other reason than the ranks are now so large and widely spread. But for the time being peace prevails outside of ideologically tinged contests for a couple of lesser party posts. Hatch, for instance, claims strong support for Baker as majority leader, saying Baker is more conservative than he appears to be.

For the first time, the western pioneers of the movement (generally from the intermountain regions inland from the Pacific Coast strip) will be outnumbered by senators from other regions, giving the group a more truly national footing and outlook. It will include representatives from such previously unlikely states as New York (Alfonse D'Amato) and Wisconsin (Robert W. Kasten). Both the South and Midwest are well-represented.

To understand those who shaped the group, however, a good place to begin is with the Rockies and Wallop, whose 1976 campaign included a television ad featuring a potty-toting cowboy to ridicule federal job-site health and safety regulations. Said Wallop the other day:

"The region is really the remaining bastion of free enterprisers in the country, and the sense of self-reliance runs very strong out there. Another reason is that the vast federal holdings there brought our citizens into more abrassive contact with the federal government than citizens of any other region. It heightened the awareness of tension between government and individuals, all of it combining to make for a very conservative constituency." i

Said McClure: "It's really the last frontier . . . drawing people who are adveturous individualistic. They're the kind of people who say, 'I may do it, but you're not going to make me do it.'"

Ironically, this same kind of don't-tread-on-me spirit may bring these senators into conflict with some of the groups that helped put them into office and that tend to demand ideological purity of their beneficiaries.

In discussing priorities for the 97th Congress, for instance, few of the senators mentioned abortion, prayer in schools or other social causes that galvanized Moral Majority and other New Right groups during the elections. Almost to a man, they said economic issues -- principally cutting taxes, government spending and inflation -- would predominate.

"The ecomony has got to come first," said Armstrong. "I don't think there is anything like the consensus among Republicans on prayer or abortion than there is on balancing the budget and cutting taxes."

Said Madsen, Hatch's administrative assistant: "We say we have a better way but we don't want to destroy what exists until we have something better ready to take its place. . . . I expect they'll go slow on a lot of the social issues and get some heavy flak from the far right, which I support, I'm a part of it."

There was also in what Madsen said -- and what several senators indicated -- an acute appreciation for the slowness with which anything can be done in Washington, including tearing down as well as building up.

"People think that as soon as you have a majority, you can change everything," said Madsen. "But the Democrats had a majority for a long time and they couldn't do anywhere near all that they wanted to do."