Ten moderate-to-conservative Democratic senators, chafing under their party's identification with liberal causes, have begun caucusing quietly in an attempt to expand their influence in Democratic councils and nudge the Senate Democratic leadership to the right.

The group is less formal and structured than the Democratic Conservative Forum (caucus) that was organized in the House after the blitzing of Democratic ranks in the Nov. 4 elections. But it reflects a similar resurgence of conservatives within the legislative wing of the party, aimed at toning down its liberal image.

According to a source close to one of the principals, the group's formation stemmed in large part from dissatisfaction with then-majority leader Robert C. Byrd's effort to win passage of fair housing legislation in the postelection session of Congress, which some conservatives interpreted as an undue tilting toward the priorities of the bill's chief sponsor, Sen. Edward M. Kenney (D-Mass.).

"We hope Byrd gets the message and recognizes that the party is not just Kennedy and Co.," he said. "Byrd operates on the squeaky wheel principal . . . and we're going to squeak."

Sen. David Boren (D-Okla.), who helped put the group together, said the effort is "definitely not a challenge to the leadership" but rather an attempt "to move our party back into the mainstream of American politics" and to offer an alternative to liberal positions at a time when the Democratic Party is regrouping in defeat.

An aide to another participant said the group is divided over "how much to buck the establishment," as well as diverse in its thinking about how "formal and public" the caucus should be. One reason for keeping the group on an informal basis is to avoid the appearance of challenging the leadership, another Senate aide said.

The group, spearheaded initially by Sen. Dennis DeConcini (D-Ariz.) as well as Boren, met for the first time last Wednesday in Boren's office and plans a second meeting next week, with relatively loose plans for further sessions in the future. Staffs of the senators are also meeting.

Senators who attended the first session or indicated support for the effort included Ernest F. Hollings (S.C.), J. Bennett Johnston (La.), Sam Nunn (Ga.), Lawton Chiles (Fla.), J. James Exon (Neb.), Edward Zorinsky (Neb.), Howell Heflin (Ala.), David Pryor (Ark.), DeConcini and Brown, according to an aide to one of the participants. Other conserative-leaning Democratic senators are expected to be contacted about joining.

Many of the participating senators have often voted with Republicans on issues such as defense, foreign policy and fiscal restraints and could provide the swing votes on such issues when the narrow three-vote Republican majority in the Senate is threatened by a bolting of GOP liberals and moderates. "But the Republicans will have to come to terms with us," said one of the aides. A likely goal is influence in shaping tax-cut legislation to assure that spending cuts accompany any tax relief, he said.

Boren said there is "emphatically no idea of forming a coalition with Republicans," however. "It is much more an attempt to pull our own party back into the mainstream," he said. There is a strong feeling on the part of the participants that they must be "a lot more vocal if the party is going to survive in the South and West," the home turf of most of the group's participants.