Senate Republicans moved last night to limit debate on the judicial nomination of Daniel A. Manion in an attempt to prevent Democratic opponents from dragging out the controversy.

As debate opened on President Reagan's choice for the 7th U.S. Circuit Court of Appeals, Majority Leader Robert J. Dole (Kan.) and other Republican leaders filed a cloture petition to cut off debate.

The petition, filed in an attempt to force a vote on Manion before Friday's scheduled Senate recess, had 21 of the necessary 60 signatures last night. Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.) urged senators, whether they support Manion or not, to vote for cloture "to bring the matter to an end."

"The nominee is entitled to have a vote by the Senate," Thurmond said.

Sen. Joseph R. Biden Jr. (D-Del.), who opposes limiting the debate on Manion, opened the long-awaited assault on the former Indiana state senator by saying that Democrats do not oppose him on grounds of partisan politics. "This is not about right to life," Biden said; ". . . it is about . . . intellectual competence to serve."

Sen. Edward M. Kennedy (D-Mass.) said, "People, just because they're born and become lawyers, don't necessarily deserve to be on one of the most important courts in the land."

But Sen. Dan Quayle (R-Ind.), a classmate of Manion at Indiana University Law School, defended the nominee's qualifications at length.

The cloture vote should provide a gauge of whether Manion's nomination is salvable; the Judiciary Committee reported it to the floor without a recommendation last month.

Before debate began yesterday, Attorney General Edwin Meese III rallied behind Manion, and officials said Reagan planned to call senators undecided about the nomination. This appeared to be the kind of intense lobbying campaign that the administration failed to mount last month when the Judiciary Committee rejected nominee Jefferson Beauregard Sessions III to be a federal judge in Alabama.

"Dan Manion's qualifications are simply not in doubt, the partisan attacks on him notwithstanding," Meese said in a statement. He said criticism of Manion for receiving the American Bar Association's lowest positive rating, as have nearly half the judicial nominees of the last decade, "represents a new low in the already unseemly ideological battle being waged against this administration's judicial nominees."

Meese expressed surprise that more than 40 law school deans have signed a letter opposing Manion as unqualified to serve as a federal judge. Meese said the deans "may have allowed themselves to be drawn into what is essentially a partisan battle."

Signers of the letter, received by Senate leaders yesterday, included deans from Harvard, Yale, Georgetown, George Washington, American, Howard, Maryland, Virginia, Duke, Columbia, Cornell, Rutgers, Michigan, Emory and Loyola. A similar letter was released from more than 100 professors at 38 law schools.

Other groups and labor unions, ranging from Common Cause to the National Council of Senior Citizens to the United Steelworkers of America, also have signed letters opposing Manion as too extreme and too inexperienced for the federal bench.

Criticism of Manion, son of the late Clarence Manion, a conservative broadcaster and John Birch Society leader, has focused on his South Bend law practice and the fact that he has never published a legal article or been the lead counsel in a federal case.

Common Cause Chairman Archibald Cox, whose organization has opposed only one other judicial nominee, during the Carter administration, said in a letter that Manion "is woefully lacking . . . both the professional background and the commitment to our constitutional system that is necessary to serve as a federal appellate judge."

Manion is in danger of becoming the first judicial nominee rejected by the full Senate since G. Harrold Carswell, President Richard M. Nixon's second unsuccessful choice for the Supreme Court, was defeated in 1970.