The White House expressed strong opposition yesterday to a demand by 46 senators for a huge budget cutback in President Reagan's proposed missile defense system, the Strategic Defense Initiative.

"We hope this is not the course which Congress will take in acting upon our budget request," presidential spokesman Larry Speakes said in a statement responding to a letter from a bipartisan coalition of senators to the Senate Armed Services Committee, which will set budget ceilings next month.

The senators called for no more than a 3 percent after-inflation increase for the "Star Wars" system, rather than the 74 percent rise that Reagan requested for fiscal 1987, the budget year starting Oct. 1.

"SDI must continue as a top national priority," Speakes said. "Cuts made in SDI funding requests last year have already slowed progress in several key areas and have narrowed the range of technologies we can explore.

"Further cuts would seriously compound these problems and set back the prospects for an informed decision in the early 1990s as to whether to proceed with full-scale development of effective strategic defenses," he added.

Speakes said the proposed missile defense system has "gotten the attention of the Soviet Union, and we think it has contributed to discussions on arms control and will continue to have an effect as we proceed with research."

The senators complained that the proposed missile defense system "has received excessive and inappropriate emphasis" in the Pentagon budget and that it is "being rushed into a premature development decision in the early 1990s in order to meet an unrealistic schedule."

Speakes said Reagan requested $3.7 billion in fiscal 1986 and Congress approved $2.7 billion; Reagan sought $4.7 billion for fiscal 1987 but Congress wants no more than an inflation adjustment over the $2.7 billion level.