Sen. Charles McC. Mathias Jr., the low-key liberal from Maryland, formally launched a campaign for a third term yesterday, and already the 57-year-old Republican looms as a heavy favorite to heat any Democrat who challenges him.

The question that worries many Mathias supporters, however, is whether he can defeat a Republican. Specifically, would enough moderate-to-liberal voters show up in a GOP primary to outnumber the hard-core right-wingers who would pour out of the woodwork if Rep. Robert E. Bauman, the conservative from the Eastern Shore, decided to challenge Mathias.

Bauman met with his closest advisers at his home in Easton yesterday and revealed that he will file for office at the secretary of state's office in Annapolis tomorrow. He would not say whether it would be a challenge to Mathias or a reelection bid for the House.

Whatever Bauman decides, the fact that the greater threat to Mathias is from within his own party tells much about the senior senator from Maryland, a political maverick who made the "enemies list" at the Nixon White House, who picked up the endorsement of organized labor eight months before he announced his candidacy for reelection, and yet who views himself as more in the mainstream of his party than ever before.

A number of state Democrats not only view Mathias as unbeatable, but as one member of the state's congressional delegation put it, "why would you want to beat him?" Yet those same Democrats agree with the House member who added, "Bauman would knock Mac off in the primary."

That prospect has many Democrats salivating. They are convinced that Bauman might win the primary but is a sure loser in the general election where the Democrats hold a three-to-one registration edge that an ideological Republican such as Bauman would have a hard time overcoming.

Indeed, with Bauman in the race, the Democrat heavyweights would surface, some from retirement. Among possible candidates mentioned are former acting governor Blair Lee III; Baltimore Mayor William D. Schaefer; former state Senate president Steny Hoyer, HUD Assistant Secretary Robert E. Embrey Jr., and Rep. Barbara A. Mikulski,, who lost to Mathias six years ago.

Without a Bauman candidacy, the Democratic nomination is likely to go to a lesser-known figure, such as state Sen. Victor L. Crawford (D-Montgomery), a declared candidate, who concedes, "it's a long shot, but it's a shot at a title, and how often do you get that?"

Mathias is viewed as so strong that Crawford acknowledges one of his problems in trying to finance a campaign is "convincing the Democratic National Committee not to write off Maryland" when it distributes money to party nominees.

"I can beat Bauman, but so can others," said Crawford, 47, a Rockville lawyer who has been in the state legislature since 1967. "Right now, however, I'm busy shutting the back door before I open the front."

Other Democrats mentioned as possible candidates, whether or not Bauman gets in, include Baltimore City Council President Walter S. Orlinsky, and state Senate President James Clark Jr. and state Senate majority leader Rosalie Silber Abrams, who also is the state party chairperson.

Crawford takes issue with Mathias' invincibility, noting that in his first race for Congress "he beat Danny Brewster, who had a lot of personal problems, and then Barbara (Mikulski), who started late and didn't have time to research the issues.

You can't out Mr. Nice Guy him," Crawford said of Mathias, "but he's really been a very bad senator. His record is a myth. I'm going to hold his feet to the fire on issues."

Marthias formally launched his campaign yesterday morning in his hometown of Frederick. Standing in the crisp sunshine on the courthouse steps with his wife and two sons, within sight of the magnificent home where his 83-year-old mother still lives, Mathias said, "This is where my roots are, this is where I began my family life and my political career." Before moving to the Senate in 1968, he served eight years as the 6th District congressman, representing an area that sprawled from the West Virginia border to Western Avenue on the District line.

Mathias then drove to the Lexington Market in downtown Baltimore, where he repeated the speech before a crowd of noisy shoppers and television crews.

Despite the glare of the television lights, Mathias told these who could hear that he would conduct "an old-fashioned campaign . . . based not on image, but on the theme that Gen. Washington sounded during a critical moment during the Constitutional Convention. 'Let us raise a standard,' he said, 'to which the wise and honest can repair.'"

After the brief speech, Mathias was given a plaque by Ray Clark, president of Local 44 of the American Federation of State, County and Municipal Employees Union.

Mathias' voting record has earned him wide support among union members. The AFL-CIO's Committees on Political Education rates Mathias second only to New York's Jacob Javits among Senate Republicans with an 11-year record of 112 "right" votes and 37 "wrong" votes. (Conversely, the American Conservative Union, of which Bauman is president, gives Mathias a zero rating and Bauman 100 percent.)

William O. Franz, general manager of the 115-stall market, then led Mathias on a tour, a Maryland political tradition that Franz has carried out with nonpartisan enthusiasm in the past for candidates Jimmy Carter, Hubert Humphrey, Morris Udall and President Ford's son Jack.

Along the way, Mathias and his family were given samples of oysters and clams on the shell, cheese, corned beef and hero sandwiches, potato chips, chocolate chip cookies, peanut brittle candy, root beer, butter pecan ice cream and hot roasted peanuts, in that order.

"You can't say you're on a diet," said Mathias, patting his girth. As he worked the crowd, he kissed two-year-old Lindsay Terziu, who cried, and embraced a number of older people, who didn't.

The day was vintage Mathias -- non-partisan, moderate, historical in perspective and, to his detractors, lacking in substance and political point-of-view.

At 57, Mathias is the picture of the country whig, greying and balding, a bit chunky, comfortable in the tweedy English sense, biting on an unlighted pipe and recalling anecdotes for every occasion. His wife, Ann, is the daughter of former Massachusetts governor Robert F. Bradford, a descendant of the second governor of Plymouth Colony. Their sons are Charlie Bradford, a Harvard College sophomore, and Robert Flake, a preppie at St. George's School, Newport, R.I.

Mathias' own heritage is Frederick County gentry, tending more to bulky sweaters and balky sheep than to riding habits and galloping horses. When he was given an honarary doctor of laws degree by Washington College in Chestertown, Md., in 1977, the citation described him as "a man of many parts, comfortable in Washington, yet happiest on his Appalachian farm, where he raises sheep and other animals."

Mathias' current biography says that "on his unfrequent breaks from the congressional routine, he relaxes on the farm named "Bullskin" because George Washington reportedly slept under a bullskin by a creek while surveying the wilderness there.

The farm's location is near Charles Town, W.Va., a detail that was markedely no mentioned during his first Senate campaign. In those days, Mathias always identified the farm as being "west of Frederick," or "near Brunswick," both of which are technically correct, but which managed to obscure the fact that his favorite hideaway is not in The Free State, but across the Potomac River in West Virginia.

The same honorary degree citation took note of Mathias' fondness for automobiles that others would have junked long ago. It said his arrival for an official function at the White House gate driving his early 1960s blue Buick station wagon, "absent a back seat because one of his feisty rams wanted to walk when the senator wanted him to ride," would "routinely bring guards and Secret Service agents on the run, as if to repel an intruder."

Mathias' easygoing manner prompts some critics to suggest that he is lazy, and indeed, he readily admits that he is no workaholic. Unless the Senate is in session, he usually leaves his third-floor suite in the Russell Senate Office Building by 7 p.m. for a 30-minute adventure (his driving skill is legendary) to his brick colonial home on Leland Street in Chevy Chase. The celebrated blue station wagon gave out after 200,000 miles, and its replacement, the senator notes with pride, is a 1973 Buick with "only 156,000 miles on it."

Another rap directed at Mathias is that he is occassionally absent-minded, disorganized and easily manipulated. A case in point occured four years ago when conservative Republicans in the Senate prevented him from moving up to ranking minority member of the Judiciary Committee.

As a result of the retirements of senators Roman Heuska, Hiram Fong and Hugh Scott in 1976, South Carolina's Strom Thurmond, the longtime ranking Republican on the Armed Services Committee, also found himself the ranking minority member of the Judiciary Committee, just ahead of Mathias.

By custom, no senator holds a ranking position on more than one committee, so it was presumed that Thurmond would give up the Judiciary slot. Instead, Thurmond switched places with fellow conservative John Tower of Texas on Armed Services, thus blocking Mathias from the top spot on Judiciary.

"The conservatives wouldn't have dared to screw Jack of Chuck the way they did Mac," a former Mathias aide said of liberal Republicans Javits and Charles Percy of Illinois.

To a potential opponent such as Orlinsky, such namuvering, and the fact that Mathias holds no ranking assignment after 12 years, is proof that Mathias lacks the clout or savvy needed to operate in the Senate.

The willingness of rivals to try to deprive Mathias of power arises from a perception that "Mac doesn't want things badly enough," one Hill observer suggested.

Four years ago, Mathias' name was placed in the GOP presidential primary by the secretary of state in Massachusetts until he asked that it be withdrawn. One Sunday afternoon, during the time he was toying with the idea of running for president, Mathias invited a reporter to talk about it at the farm. Warmed by martinis and a blazing fire, the conversation quickly drifted away from the presidency to anecdotes about farms and Maryland history.

This year, Mathias is being mentioned as a possible vice presidential running mate of several of the GOP contenders. Mathias has something positive to say about all of the hopefuls, but reserves his warmest praise for George Bush. He depicts Bush as "very conservative, just to the left of Reagan and Crane, but George and Barbara are personal friends of Ann and me."

A Bush-Mathias ticket would have both regional and philosophical balance, it is suggested.

"If I had aspired to national office in 1980," Mathias answered, "I wouldn't have put myself and my friends on the line" by announcing for reelection so early.

But then, with a twinkle in his eye, Mathias recalls the words of John Sherman Cooper -- there is seldom an occasion for which Mathias doesn't have a quote or a story -- saying the former Kentucky senator once advised him, "Never let them count on you -- don't be predictable."