The U.S. Navy, in a billion-dollar version of every basement boat-builder's nightmare, is constructing a ship apparently too big to get out the door.

The vessel is the mammoth new missile-firing Trident submarine: longer than the Washington Monument is high, and - evidently - six inches deeper than the Thames River channel here, where it is scheduled to be launched next year.

Spokesman for both the Navy and the Electric Boat Division of General Dynamics, which is building the Triden, say this is really not a problem.

Though its sea trial does exceed the 36-foot depth of the channel, it will be "technically feasible" to get the submarine to sea, with adjustments in loading, according to Spencer Reitz, assistant general manager of Electric Boat.

But an official Navy Department memorandum obtained by The Washington Post says Electric Boat advised the Navy's superintendent of ships in Groton last March that the Thames channel "was not adequate for the Trident transit between the building yard and the sea.

"Additionally," the memo said, "Electric Boat advises that safe transit of the Thames River channel for Trident vessels can be assured only if the channel has a maintained depth of 40 feet below mean low water."

Sea trial draft of the Trident the memo says, is "calculated by Electric Boat to be 36.5 feet."

Just how the potential mismatch between the Trident's draft and the channel's depth remained so long unnoticed is not altogether clear.

The new submarine, successor to the Polaris-Poseidon series, is no small project. It is the most expensive weapon in history, and has been under development for 12 years.

Fourteen of the huge subs have been ordered so far - seven of them with the Electric Boat Division, which employs some 24,000 people. Last December the Navy said the first of the vessels being built here was running 50 percent over its estimated cost and now wears an anticipated price tag of $1.2 billion

The Navy moreover, has just finished spending four years and some $3 million dredging the Thames channel to 36 feet, though it has known for at least that long that the Trident would need more water on its way to sea.

The key stretch of channel in question extends roughly 2 1/2 miles from the building docks of Electric Boat on the east bank of the Thames south to the deeper water of Long Island Sound.

Although the vagries of outfitting a new and complex ship make timetables uncertain, the Trident is scheduled to travel that section when it departs for sea trial sometime in mid-1980.

Since tides here normally run about 2 feet, the Trident could, theoretically, be floated or towed out at high tide with 1 1/2 feet to spare. The question, according to the memo, is whether that is enough of a safety margin for a billion-dollar weapons system with a nuclear reactor on board.

The Navy, in an official statement on the subject last week, said "variations of the loading of the Trident during sea trials and deliverycan decrease the draft by several feet," and insisted that "the Trident submarine will be able to transmit the Thames River channel."

But an engineering consultant in Washington who has worked extensively on the loading problems of the submarine said lightening the 18,700 ton vessel would be "a major engineering hassle."

Unlike conventional ships with cargo hatches and fuel tanks, he said, the Trident is being largely built and fitted out in three sections, which will be welded together before launch.

With the exception of the 24 nuclear missiles, each of which has its own hatch on deck, "everything not welded inside before launch will have to fit through a six-foot logistics batch. Moving enough weight in and out of there to life a ship that size a few is not going to be easy. There are something like decks in that submarine," he said.

While many conventional ships can pump their fuel tanks out to lighten their load, the fuel and propulsion weight of the Trident's 90,000 horse-power nuclear reactor will remain virtually constant.

Electric Boat executive Reitz, while repeating that it would be "no problem" and " technically feasible" to get the Trident to sea, said he couldn't say just when questions first were raised about the adequacy of the Thames channel.

But he said he was "aware rather recently of a meeting with the Navy" about the subject. The meeting, he said, was about just "how it would be technically feasible" to get the Trident to sea . He was not aware he said, of any meeting or discussing of the subject before that.

The Navy, however, says the Thames channel depth has been " a subject of continuing review," and adds: "The most recent information available is under review by the Naval Material Command to determine if any further action is required...

"Limitations of tide and ship conditions during [the Trident's] sea trials as well as the silting process of the river are being reviewed continuously," the Navy adds. "It is possible that this review will identify the need for further dredging of the channel to accomodate Trident."

The memo obtained by The Post - dated April 21, 1978, and signed by Capt. E.M. Peebles, "project manager of the Trident submarine ship acquisition project" - is more specific:

"NAVSEA 07 has requested technical assistance and advice from COMNAVFAC to determine the most feasible and expeditions method of increasing the Thames River channel depth to the required 40 feet."

If further dredging proves necessary, the primary difficulties should be financial and bureaucratic rather than physical.

Dr. John Dowling, a University of Connecticut geophysicist who has worked extensively on the Thames River channel, says the silty clay bottom is relatively stable and easy to dredge. Bedrock lies a good 150 feet or more below the bottom, Dowling said.

But the process of applying for a dredging permit, filing an environmental impact statement and doing the dredging would clearly require more than a year. And the Navy says it has no money in the 1979 budget request for channel dredging.

Meanwhile, according to the April 21 memo, the Navy has been investigating a further complication: the 560 foot Trident may be too long to make a scheduled turn in the channel on its way to the fitting-out pier after launching.

"NAVSEA (PMS396) has initiated action," thememo says, "to determine if a problem does exist."