New York Gov. Mario M. Cuomo may end up with millions of just-in-case dollars left over from his reelection campaign this year that could be put to use in a campaign for the 1988 Democratic presidential nomination.

Cuomo's son and political adviser, Andrew, said, "He's not running for president," but added that a shift of funds "could be done."

Cuomo's campaign committee has almost $8 million in the bank. State Democratic executive director William Cunningham said the reelection campaign most likely will spend $5 million or $6 million, and might get by on $3 million, the amount Cuomo's Republican challenger, Andrew O'Rourke, the Westchester County executive, hopes to raise and spend. So far, O'Rourke has raised about $400,000.

Spokesmen for the state Board of Elections and the Federal Election Commission agreed that a transfer of funds from a Cuomo state campaign fund to a federal election fund is not prohibited by state or federal law. Fred Eiland of the FEC said there are different limits on contributions for federal and state elections and that this could cause bookkeeping headaches. Moffett Loses Showdown

Former U.S. representative Toby Moffett (D-Conn.) faced a showdown yesterday with Gov. William A. O'Neill at the state Democratic convention -- and lost.

Moffett fell 20 votes short of the 270 needed to keep his candidacy alive and force O'Neill into a primary that would have been held in September.

O'Neill, who had been assured the convention's endorsement, won the nomination outright by polling 1,098 delegates to 250 for Moffett.

After months of fighting for delegates, the bitterness in the O'Neill-Moffett race was apparent as the governor's supporters booed Moffett when he stood at the lectern to speak.

In addition to renominating O'Neill, delegates to the state the Democratic convention also nominated Sen. Christopher J. Dodd for a second six-year term. New Image for League

The 66-year-old League of Women Voters, best known for sponsoring political debates and registering voters, has a new president who thinks it's time for a change in image. "Being nonpartisan does not mean being nonpolitical," Nancy Neuman said.

"We will risk being controversial as we become more vocal about public policy issues." The league has been promoting tax revision and opposing funding of the Strategic Defense Initiative. She said it intends to pay special attention to issues concerning women and poverty.

Along with its new president, the league has its first male executive director and a new direct-mail campaign -- asking each member to recruit one person this year -- to boost membership, which has declined from 157,000 to 110,000 over 25 years.

The league will fight to keep sponsorship of the presidential debates, which it has handled since it brought challenger Jimmy Carter and President Gerald R. Ford together in 1976.

Both major political parties have moved to take over that role. Neuman said, "We don't think the two political parties can sponsor nonpartisan debates. You need an honest broker to run between the candidates' camps." Four More Years?

Rep. Guy Vander Jagt (R-Mich.), chairman of the National Republican Congressional Committee, thinks big: he wants to amend the Constitution so President Reagan could run for a third term.

Vander Jagt enclosed in his latest fund-raising letter an "Official Constitutional Petition" that "calls for the immediate repeal of the 22nd Amendment which limits a president to only two terms." Vander Jagt writes that if he receives enough petitions, he "will personally introduce the legislation to repeal the 22nd Amendment on the floor of the U.S. House of Representatives."

Vander Jagt adds, "there are a number of exceptionally well-qualified Republican presidential candidates . . . . But why shouldn't we hold on to the 'original' as long as possible?"

He explains that "to print and distribute more petitions as well as give our candidates assistance . . . I hope to raise no less than $2.1 million."

And just in case anyone has "any doubts about sending at least $20," Vander Jagt reminds them that keeping Reagan in office is "worth at least a $20 investment now. CAPTION: Picture 1, Gov. Mario m. Cuomo . . . has nearly $8 million in bank; Toby Moffett. Fell 20 votes short in challenge