BECAUSE OF the way they intend to rearm America and use military power around the world, President Reagan and Defense Secretary Caspar W. Weinberger have put themselves on a collision course with the old maxim that he who tries to be strong everywhere ends up being weak everywhere.

The last American leader who found himself in this predicament, ironically enough, was Lyndon Johnson's field commander in Vietname, Gen. William C. Westmoreland. His plight in trying to win that small war in that small country, where the United States had vastly superior weapons, casts doubt on whether the new Reagan-Weinberger "fight anywhere and everywhere" strategy could be carried out.

It "would have required literally millions of men" to combat the guerrillas in the villages as well as take on the main force units elsewhere, Westmoreland wrote in his post-audit on the Vietnam War, "A Soldier Reports." "I never had any prospect of those numbers. In any case, it would have been perilous to ignore the undisputed military canon that to try to be strong everywhere is to be weak everywhere."

A platoon of professionals at the Pentagon who have watched defense secretaries come and go over the years contend Reagan and Weinberger paid no heed to that canon as they hastily rewrote former President Carter's final two military budgets and issued a series of secret directives on what they expected the armed services to be able to do in the world.

Their new marching orders call for reequipping the Army and expanding it by 96,000 troops; speeding up construction of Navy ships, including $3 billion Nimitz nuclear aircraft carries which Carter opposed; buying new bombers for the Air Force along with the MX missile and larger quantities of fighter aircraft; giving the Marines the ships they want for taking them and their equipment to distant trouble spots like the Persian Gulf; gearing up the defense industry to handle an eightfold increase in military orders in a period of tension and up to half the gross national product in an emergency; readying the services for extended fighting with the Soviets and/or their surrogates all around the world, not just in the area of conflict.

The cost of doing all this and more already is rising above the administration's projections. Deputy Defense Secretary Frank C. Carlucci has acknoledged publicly that "the tail" from Reagan's additions to Carter's fiscal 1981 and 1982 defense budgets is pushing the fiscal 1983 budget $10 billion higher than anticipated. Paying for this "tail" in fiscal 1983 and beyond will require Reagan to strain the nation's pro-defense constituency by asking Congress to raise the defense budget by 9 percent a year after allowing for inflation, not the 7 percent the president had in mind. the things the generals and admirals felt sure they would get under Reagan.

"This place is about to blow up," said one Pentagon careerist who has seen just how much money would be required in future years to carry out the hastily drawn Reagan-Carter blueprint. He said the cuts needed to stay within 7 percent annual growth limit will have to be deep and painful. He predicted the old-fashioned interservice fights for money will erupt soon even though Reagan is the most generous commander-in-chief military leaders have ever had in peace time. Civilians would have to referee such fights, undercutting Weinberger's pledge to let the services run their own affairs with minimum interference from his office.

But bringing the soaring costs of the Reagan-Weinberger budget under control will not be just a matter of making cuts inside the Pentagon. Congress will have to go along for them to stick. And this is never easy. Generals and admirals say the deleted weapons are needed. Defense contractors warn that jobs and votes are at stake. Politicians add money to the Pentagon budget to pay for weapons built in each other's home areas in a log-rolling process that gains momentum as it goes along. Pentagon frustrations in trying to reduce these procurement accounts often drive defense secretaries to cutting monies for flight training, for spare parts, for field exercises, for maintenance. But if Weinberger does this now, he risks reading the same kinds of news stories that helped Reagan defeat Carter: planes that cannot fly for want of parts; Army units and Navy ships unready to fight.

Some pro-defense congressional leaders sense that the Reagan administration bit off more than it can chew. This will embolden them to drown defense blueprint of their own next year rather than continue to follow Reagan's. Sen. Ernest F. Hollings (D-S.C.), former chairman of the Senate Budget Committee which pressed for higher defense spending, typified the congressional complaints about Reagan and Weinberger trying to do too much too soon. Said Hollings on the floor shortly before the August recess:

"Mr. President, the only conclusion can be that this administration is uncertain about where it is going on defense policy. Not only does it lack plans for implementing the programs, but it is unclear as to the program priorities. We are told of all the many programs

In what may represent some second-thoughts about the wisdom of trying to be strong everywhere, Reagan refused to go along with the extra 2 percent. This means that some of the programs he portrayed a few months ago as vital will have to be cut out of the Pentagon budget submitted to Congress next year. Even the $1.5 trillion he told Congress he wanted to spend on defense over the next five years -- a record amount for peacetime -- is not proving to be enough to buy all the Department of Defense would like to buy. So Congress inevitably comes face to face with the fundamental question: Can we afford all of the programs that the president and Department of Defense have said are necessary to make significant improvements in our armed forces? I believe the answer is resoundingly 'no' when consideration is given to the flawed estimates of the administration concerning inflation in the defense business and to the uncontrolled management and spending practices of the Department of Defense."

While Hollings, Chairman Mark Hatfield (R-Ore.) of the Senate Appropriations Committee and others are contending there will not be enough money to pay for Reagan's "fight anywhere" preparations, another group of influential politicians is mobilizing to challenge hoe Reagan intends to spend these new billions -- not how much he will spend. Called the Reform Caucus and composed of such pro-defense lawmakers as Sen. Sam Nunn (D-Ga.) and Rep. G. William Whitehurst of Virginia, second-ranking Republican on the House Armed Services Committee, they intend to force the Reagan administration to consider alternatives to the Cadillacs of weaponry -- cheaper diesel submarines to supplement nuclear submarines, for example.

Besides trying to get more bang for the buck, the members of the Reform Caucus are arming themselves against the backlash they see coming in election year 1982 from voters who feel Reagan spent too much on guns, without getting many delivered, and too little on butter. If the backlash indeed comes, Reagan may end up feeling like Westmoreland -- a commander who tried to cover too many fronts.