An influential Republican, Sen. Robert J. Dole of Kansas, said yesterday he thinks the Senate will cut twice as much as President Reagan wants from the fiscal 1982 defense budget.

Although Dole did not say it, this would leave Reagan's defense budget lower than that proposed by Jimmy Carter for 1982.

Reagan is scheduled to hold a news conference tomorrow at which defense is certain to be one topic; it will be his first full-dress news conference since June 16. Then on Friday, the White House said Reagan will announce his decisions on which new strategic weapons systems he wants built, and in particular his decisions on the MX missile and B1 bomber.

Dole said that he does not know what Reagan will do strategically, but said of the president's $1.5 trillion five-year defense program: "Some of us wonder if the Department of Defense can spend money that fast wisely."

For fiscal 1982 alone, Reagan has recommended limiting cuts in his defense budget to $2 billion in spending and $7.6 billion in budget authority. Dole said in an interview yesterday that the Senate will insist on deepening the spending cut to between $4 billion and $5 billion for fiscal 1982. Even so, the budget would grow mightily from the fiscal 1981 levels.

"From just visiting around with people," continued Dole in relating recent conversations with fellow senators, "I think the feeling is that before we go back to any committee for another share of cuts, let's make certain we haven't overlooked someone."

That "someone," Dole said in giving the view of committee chairmen he had talked to, is the Defense Department. "If we are going to accomplish our goal" of balancing the federal budget by 1984, "we can't have Defense bringing up the rear."

Dole's public warning to Reagan is politically significant because he has been a stalwart for the president as chairman of the Senate Finance Committee. In that job, Dole has delivered some of the hardest cuts to achieve, including in Social Security, medical assistance and welfare.

Stressing that he agreed with Reagan that the United States "has got to catch up" with the Soviet Union militarily, Dole said at the same time that the Pentagon must carry a larger share of the load in the government-wide effort to reduce the federal deficit.

"We've got a difficult job finding any more cuts in so-called social programs. There's a matter of perceptions out there too," said Dole in referring to voters who perceive that lawmakers are spending too much on guns and too little on butter.

Asked if the report the Pentagon released yesterday on Soviet military might would make a difference in that perception, Dole said "there's not very much impact here" in the Senate.

Then-president Carter recommended spending $180 billion on defense in fiscal 1982. Reagan raised that total in March to $184.8 billion. The Reagan administration's midyear economic review lowered the figure to $183.8 billion. Now Reagan wants to cut that total another $2 billion, lowering fiscal 1982 defense spending to $181.8 billion.

If Dole and his allies succeed in imposing a cut of $4 billion rather than the $2 billion Reagan has recommended, the president's defense spending for fiscal 1982 would go down to $179.8 billion--less than Carter had in mind.

Rep. Jack Edwards of Alabama, ranking Republican on the House Appropriations subcommittee on defense, said in a separate interview yesterday that the $4 billion to $5 billion cut Dole figures "is inevitable but nobody wants to say it. His sense of the congressional mood is about right."

Besides cutting deeper than $2 billion in fiscal 1982, Edwards predicted that Congress will rewrite much of Reagan's defense budget for that year as it imposes its own sense of priorities in apportioning the reduced total. The House subcommittee is expected to start marking up the Pentagon's fiscal 1982 appropriations bill in mid-October.

Asked if the Pentagon's release of the report on the Soviet buildup would help or hurt congressional deliberations on how much the defense budget should be cut, Edwards replied that the reactions would neutralize each other.

The hawks, he said, will see the report as a confirmation of their fears, and the skeptics will say: "What did you expect? It's markup time."