The assistant leader of the Senate Democrats predicted yesterday that the MX program will be approved by Congress in test votes next week, but that the number of missiles later will be cut below the level President Reagan is seeking.

Sen. Alan Cranston (D-Calif.), an opponent of the MX, said Reagan's argument that he needs the weapon as a bargaining chip at the Geneva arms talks "has worked." But Cranston predicted that when a vote comes up later this year on financing additional MX procurement, "the president will get significantly less than the 100 missiles he wants, perhaps closer to 50."

MX opponents have focused their hopes on the Senate, where Democratic gains last November gave them reason to believe that there may be enough votes to kill the program. Vice President Bush's tie-breaking vote narrowly averted that decision in 1984.

Reagan has been lobbying hard for congressional approval of the MX, and Cranston said he is convinced that the president "sincerely wants an arms control agreement. It's a deeply held conviction, almost a moral impulse on his part."

Cranston said he opposes the MX because "it can't be both a bargaining chip and something we need."