The Senate's Democratic and Republican leaders said Tuesday they would move to limit debate on the superpower medium-range nuclear missile treaty and predicted it could be approved before President Reagan meets with Soviet leader Mikhail Gorbachev next week.

Senate Majority Leader Robert Byrd, D-W.Va., said he would offer a cloture motion today to cut short the long series of amendments being offered by a small band of conservatives who oppose the pact."It is conceivable that we could finish the work on the treaty by Friday or Saturday," Byrd said outside the White House after a bipartisan leadership meeting with Reagan. "The chances now are pretty good," he added. "There's no reason why we should have continued delay for the sake of delay."

Byrd's Republican counterpart, Sen. Bob Dole of Kansas, said he supported the move to cut debate, and quipped that perhaps the way to do so would be to have Reagan "take Jesse with him" to Moscow, a reference to Sen. Jesse Helms, R-N.C., the leading treaty opponent.

Reagan "said he'd have to ride on the wing," Dole cracked, "and somebody else said the right wing."

Helms and another opponent of the accord, Sen. Gordon Humphrey, R-N.H., showed no signs of backing off from offering a long series of amendments to the treaty, despite an appeal on Monday from Secretary of State George P. Shultz.

"I am at pains to understand why this administration, which is my administration, has become such a bunch of nervous Nellies when it comes to going back to Gorbachev to work out obvious defects in this treaty," Helms said.

"I don't care whether we offend him or not. Let's get it right the first time." Speaking of Reagan, he added: "I think he's wrong on this treaty, I think he's been misled . . . My conscience will not allow me not to pursue the obvious defects of this treaty."

Shultz went to Capitol Hill to deliver the message that the Moscow summit, which starts in just five days, will be diminished if Reagan is deprived of the vote of confidence that positive Senate action on the treaty would give him.

"There is a time to inquire and there is also a time to vote," Shultz told reporters after a meeting with 17 Republican senators. "It would be a good thing to have it."

Helms was invited to the Shultz session but did not show up. And when Dole asked Helms how many amendments he would offer to the treaty, Helms declined to say.

Three amendments offered by treaty opponents were defeated on Monday, bringing to nine the number of attempts to change the document's language that have been beaten back by the Senate since it was brought up for consideration a week ago.

First, the lawmakers voted 81-13 to kill a Helms amendment that would have required the president to certify as accurate a Soviet report on the number of triple-warhead SS-20 missiles to be destroyed before the treaty could take effect.

The Senate then voted 68-26 against an amendment by Sen. Malcolm Wallop, R-Wyo., that would have required a change in the treaty's text to eliminate what he said was a loophole that would have permitted construction of some Soviet missiles.