President Reagan is having trouble selling his big new weapons program and the reason, I submit, is that he keeps on trying too hard. There is a good case for an increase in the military posture of the United States. Hardly any serious student of the matter doubts that the increase in Soviet military power during the Nixon, Ford, and early Carter administrations went too far for the comfort of the rest of the world.
The case for replenishing the American arsenal with new and more weapons was made and accepted during the Carter administration. It was set in motion while Mr. Carter was still President. There has been a relative improvement in the Western position in the world balance of power since Mr. Reagan took office because of programs initiated by his predecessor.
The effect of the new Reagan proposals is mostly still to come.
But that is not the way Mr. Reagan tells it.
Anyone casually reading his speech would get the impression that no one had done anything about modernizing US military forces for the 10 years preceding his arrival in Washington. For example, he asserted that ''the United States introduced its last new intercontinental ballistic missile, the Minuteman III, in 1969.''
Since 1969, in 1980 to be precise, the US Navy's new Trident submarines came into service carrying new MIRVed warheads with a range of 7,400 miles.
New and heavier warheads (Mark 12A) with an accuracy rating better than any in the Soviet arsenal (a CEP rating of 220 meters against 300 for the best Soviet warheads) have been fitted into 300 Minuteman III vehicles.
A new and more accurate missile for the Trident submarines is supposed to be nearly ready for deployment.
Cruise missiles have been through the research and development stage and are ready for deployment this year. A cruise missile when launched from a long-range aircraft which is based in the US becomes, in effect, an inter-continental missile (although not ballistic).
Add that the Trident submarine is itself a matter of awe and admiration among navies the world over.
The US is not as far behind the Soviets as Mr. Reagan makes it sound.
Then, he uses arguments to bolster his case which are sometimes irrelevant and often stretch credulity. For example, in his big selling speech of last Wednesday night he cited as a mind-chilling fact that a 10,000-foot runway is being built on the Caribbean island of Grenada. He says the airstrip is being built by ''the Cubans with Soviet financing.'' Well, perhaps Cubans and Soviets are involved. But so, too, are the World Bank, located in Washington, and several American companies based in Florida.
Besides, in the Caribbean these days an island has to have a big runway to get the tourist trade. If an island has a 10,000-foot runway, it can get the big four-engined airliners with tourists in the mass. That means millions invested in big new hotels.
Add that if the Soviets were so foolish as to send any of their bombers to that airstrip they would be providing easy targets for US weapons.
Another argument he used was a photograph of a Soviet intelligence communications facility in Cuba. So what else is new? The US and the Soviets have for years ringed each other wherever they can with intelligence communications facilities. Each gets as close as possible to the other. The US has them in Turkey, Norway, South Korea, and China. Each flies reconnaissance over the other's air space, constantly. It is not new or unusual.
Finally, Mr. Reagan has loaded his program with more new weapons than logic and reason seem to justify. Many question the need for a new generation of manned bombers when cruise missiles, unmanned, are about to come on line. And to this extravagance he has now added the idea of reaching for anti-missile defense which most scientists seem to think is pure pie in the sky, and not a good idea at that.
A carefully considered case based on sound reasoning can, could, and should be made for replenishing America's arsenal. But when it is made with extravagant , inaccurate, and irrelevant arguments the result is likely to be precisely what the public opinion polls now show - a public which thinks that the arms budget Mr. Reagan is proposing costs too much - and smacks too much of handouts for the private defense contractors.
There is resistance which is certainly unnecessary due to too much careless hard sell.