NEW YORK VOTERS may soon be called upon to witness a shotgun wedding between the state's Liberal Party and Illinois Rep. John Anderson. If it does come to pass, it could be a grave blow to President Carter's chances of carrying New York and maybe even of his winning reelection.

New York's Liberal Party, suffering in recent years from electoral-sclerosis, sees a lot in the national unity ticket of Mr. Anderson and former Wisconsin governor Patrick Lucey. Ballot position in New York elections is determined by the party nominee's showing in the most recent gubernatorial election. For many years, the Liberal Party was on the third line. But in 1978 Democratic Gov. Hugh Carey received only 123,457 votes on the Liberal line -- fewer than both the Conservative and the Right-to-Life gubernatorial nominees received. The Liberal Party dropped ingloriously to the fifth line on the ballot.

Just 20 years ago, the Liberal designation was avidly courted by Democratic presidential candidate John Kennedy, and for good reason: the Kennedy-Johnson ticket carried New York by 383,000 votes, and the Liberal line provided the Democrats with 406,000 votes. But by 1976, the Liberal Party, which had lost its third line to the New York Conservative Party some 10 years earlier, cold muster only 145,000 votes for Jimmy Carter while the Democrats were carrying the state by 288,000 votes. Predictablly, the Liberals' decline at the polls led to a loss of influence among the pols.

Someone may right now be asking what a straight-forward fellow from Rockford, Ill., like Rep. John Anderson could possibly find in common with patronage addicts like the New York Liberals. The answer: They have a line on the November ballot and that's what John Anderson most needs now in New York. For a candidate to win New York ballot position without an existing party's sponsorship means the expenditure of much money, time and energy in securing signatures and fighting court challenges. The Liberals mean an awful lot of saved time and torment for the Anderson-Lucey campaign.

Some senior strategist at Liberal headquarters is undoubtedly plotting something else this very moment. If Sen. Jacob Javits were to lose Tuesday's Republican primary, Mr. Javits would still be on the November ballot as the Liberal candidate. Then with both John Anderson and Jacob Javits running on the Liberal line, who knows how many voters would pull the Liberal lever? As the wise person remarked, even in sophisticated New York all business is local.