The House Budget Committee recommended and the House has approved a 4 percent after-inflation increase in defense spending next fiscal year. The percentage was reported incorrectly yesterday.

President Reagan invited about 25 House members to dinner at the White House last night as part of an intensive lobbying campaign to win a crucial, but not final, House vote on the MX missile today.

The outlook was that Reagan would win the battle on the MX vote today, but not necessarily the war for the 10-warhead missile or the rest of the Pentagon budget now entering a series of tests in both the House and Senate.

The House is voting today on whether to release $625 million in MX basing and flight testing funds that Congress held back last year in the controversy over the "Dense Pack" basing system, which would pack the missiles so closely together in silos on the Wyoming prairie that Soviet warheads attacking the field in tight formation theoretically would destroy each other as they detonated.

"I still think the MX could lose," said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), an opponent of the missile, at the outset of yesterday's debate. But vote-counters in both parties predicted the loss would not come until after the Memorial Day recess, if at all, given the political middle ground Reagan has seized.

Rep. Jack Edwards (R-Ala.), ranking minority member of the House Appropriations defense subcommittee and floor manager of the MX resolution, acted in yesterday's debate like a man who was sure he had the votes in his pocket. He left it largely to Democrats to argue among themselves.

Rep. Joseph P. Addabbo (D-N.Y.), who led last year's successful fight against the MX, contended yesterday that it would be foolish to spend $22 billion on putting 100 MX missiles in existing Minuteman silos which the Air Force said the Soviets could destroy.

"Why should the Soviets come to the bargaining table if they know we have a vulnerable weapon?" asked Addabbo in contesting the argument that threatening the Soviets with silo-busting MX missiles would make them more willing to negotiate reductions in such first-strike weapons.

Rep. Les Aspin (D-Wis.) went to the well of the House time after time to rebut the arguments of Addabbo and others.

He said that the Reagan package--100 MXs and the promise to develop a small, mobile missile in hopes that it would inspire both the United States and the Soviet Union to step back from silo-busting, multiple-warhead missiles--was the best that could be fashioned and should be approved.

In an interview Aspin added:

"The politics of this are important. It is important for Democrats not to be the ones that kill the MX."

The Air Force had asked for $560 million for MX basing and $65 million for flight testing. This $625 million will be used to prepare 100 Minuteman silos to accept the MX and to conduct at least one flight test if the resolution is passed.

Edwards was among those who acknowledged that today's vote will be just one of several tests on the MX. The tougher tests, he said, will come when Congress votes on fiscal 1984 authorization and appropriations bills containing funds to keep the MX in production.

"The real battle is coming the week of June 6 on the procurement money," Edwards said. "I have a feeling the procurement issue is going to be closer than this."

Beyond the MX, there are wide cracks in the congressional support for Reagan's rearmament program. Edwards is one who is warning that the military services have started so many projects that there will be "a huge bow wave" of bills piling up for payment late in this decade unless cancellations, stretch-outs and cuts are imposed now.

The House Armed Services Committee, bowing to congressional protests that the Pentagon is asking to do too much too soon, has reported a bill structured to limit the "real" increase in military spending between fiscal 1983 and 1984 to 6 percent rather than Reagan's recommended 10 percent. The House Budget Committee has proposed an increase of 7.5 percent.

In the Senate, the Budget Committee has called for an increase of no more than 5 percent