Joel W. (Jay) Solomon, head of the General Services Administration, has a problem - 977,589 silver dollars worth and estimated $15- to $16-million. Each coin ultrasonically sealed in plastic, comes in a blue box with a message from the President and is ready for sale to the public.

The problem is that it's from the wrong President.

The signature at the end of the message is that of Richard M. Nixon, not Jimmy Carter, although if Solomon has his way, Carter will get into the act as well.

Because the cost of repackaging the nearly one million Bicentenial momentoes would be prohibitive, the GSA chief hopes to sell them off as is, simply attaching a sticker describing the action as "in the interest of saving the taxpayer money" - a favorite Carter theme.

"The President hasn't cleared his signature on it, that's my idea. But he has cleared the sale, Solomon said yesterday.

The way Solomon tells is, shortly after he took office in may, an aide sent him a memo about the coins which are in the custody of the Bureau of the Mint in San Francisco.

They are what remain of three million uncirculated Carson City silver dollars, which bear the "CC" mint mark and are known as the Morgan Dollars (for their designer, George T. Morgan).

Produce in the government's Nevada facility for only 13 years during the latter part of the 19th century, the coins were discovered by GSA in 1964 during an audit of the Treasury Department's silver dollars. By then, silver was no longer used to mint coins or to redeem silver cerificates.

In 1970, the coins were packaged with a presidential message looking ahead for 1976: "As we approach America's Bicentennial, this historic silver dollar is one of the most valued reminders of our national heritage." It was signed "Richard Nixon," who then looked forward to a second term ending in the country's 200th year.

Offered by GAS in five staggered lots over the next four years so that the coin market would not be adversely affected, 1,959,428 coins were sold, grossing $60.3 million. The coins brought an average price of $30 a piece, with all proceeds going to the Treasury.

The last lot was sold in June 1974, two months before Nixon resigned. The GSA said yesterday that the coin sales were halted not because of Nixon's Watergate troubles but because officials decided the coin market and been "temporarily saturated."

Meanwhile, Nixon left office, Gerald R. Ford moved into the Oval Office and the 977, 589 silver dollars languished in the valut. Then this spring, the coins came to the attention of the Carter adminstration and the new head of the GSA, whose responsibility it is to dispose of government property.

A Tennesseean who made millions developing shopping centers, Solomon's business acumen alerted him to the marketability of the coins. He was convinced that the coins should be sold to make money for the government, despite the packaging problem.

"I was at a dilemma as to whether we should unpack the silver dollars or sell them as is," he said. "To re-package them would cost somwhere between $300,000 and $1 million."

So he sought guidance from the White House. He spoke to Carter aide Hamilton Hordon (who was surprised to learn that the coins existed), and Jordon got presidential clearance ot sell the dollars as package.

"When I told them the cost of unpacking the coins, they said sell them as they are and put the money in treasury," Solomon said.

GSA, he said, will now seek congressional permission to add a sticker with a message from Carter, the cost of which Solomon estimates as "very cheap - between $25,000 and $30,000."

THe majority of the dollars are these could sell for about $15 each.

Meanwhile, the coins' political value is not exactly lost on Solomon. "I think it'll go over big as a Nixon souvenir," he said.