Senate Republican leaders failed yesterday to knock the props out from under the Senate floor fight of Democratic presidential candidate Sen. Gary Hart (D-Colo.) against the MX missile, even as President Reagan was bidding for support of the controversial new weapon with a renewed claim of flexibility on arms control.

With both houses of Congress facing votes this week on funds for the first 27 MX missiles, Reagan reiterated in his weekly radio address that "the number of missiles could certainly be adjusted downward" if the Soviet Union agrees to "deep reductions" in its land-based missile force.

"As opportunities permit, the U.S. position will continue to evolve," Reagan said from his weekend retreat at Camp David, Md. "The United States will negotiate patiently but urgently and always in good faith. But, we cannot and we must not settle for less than genuine, mutual and verifiable arms reductions."

Reagan added, "When the Congress reaffirms its support for this program and authorizes the funds to modernize our strategic deterrent, our agenda for peace will be strengthened even further."

Presidential aides said that Reagan wanted to signal Congress that his administration is genuinely interested in arms control but noted that the address had been carefully screened by national security advisers to make sure that the president wasn't signaling any concessions to the Soviets.

Arguing that production of the MX would not advance arms control, anti-MX senators continued a series of sporadic speeches in a rare Saturday session called by GOP leaders in an effort to grind down what one of them called Hart's "grandstanding" on the issue.

The Senate is expected to approve MX funding eventually. But the leadership yesterday failed to trap Hart into a potentially embarrassing test vote that it said would show that he has nowhere near the votes to defeat the MX.

To force such a test, Armed Services Committee Chairman John G. Tower (R-Tex.), in a surprise move late Friday, called up an amendment to delete $4.6 billion for the MX out of a pending $200 billion defense authorization bill and urged the amendment's defeat. But Hart outfoxed Tower by joining him in an 88-to-4 vote against the proposal, thereby rendering it meaningless as a real test of sentiment on the MX.

Tower said that the vote nonetheless demonstrated that the Hart forces "simply don't have the votes . . . they didn't want to demonstrate their own weakness." However, Majority Leader Howard H. Baker Jr. (R-Tenn.) had said in advance that the vote probably wouldn't mean anything.

Baker also conceded that Hart has probably succeeded in holding up the Senate vote until after the House, where the fate of the MX is in doubt, votes on missile production funds this week. Hart has denied that is his objective but acknowledged that a House vote against the MX "would be nice."

"If Sen. Hart's objective was to delay until after the House voted, he's probably accomplished that," Baker said. "If his objective was to defeat the MX, he's probably damaged it . . . because he's put us through several days of useless work." Baker added, "I'm resigned we're not going to finish this in a timely fashion."

The on-again, off-again debate on the MX, largely put aside yesterday for votes on other defense issues, appeared to be a test of wills as well as a fight over producing the huge new missiles and deploying them in Minuteman silos.

Asked why the Republican leadership has not tried to force a showdown by filing a debate-limiting cloture petition, a Republican aide said that such action would suit Hart's purposes. "Gary Hart is not the leader of the Senate; Howard Baker is . . . . Howard Baker is not running for president; Gary Hart is."

While acknowledging that he has never filibustered, Hart has said he would be doing what he's doing regardless of his ambition to be president.

A Democratic aide said that the ai-MX bloc's strategy is to force the Republicans to resort to a cloture vote, which would require 60 "yes" vot debate. When flight-testing for the MX was approved in May, it got 59 votes.

In the Democratic response tos, Sen. Patrick J. Leahy (Vt.) accused Reagan of sending an "inexperienced or uncommitted" team of negotiators to bargain with theSoviets and ridiculed a negotiator's suggestion that the United States not deploy 100 MX missiles in exchange for destruction of 650 Soviet rockets. "As we say in Vermont," Leahy said, "that's like offering to swap a moo for a cow."