May 10, 1981

NASSAU Democrats, who were having trouble finding a candidate for County Executive, now have two men fighting for the nomination in what looms as a potentially damaging primary contest. John W. Matthews of Long Beach, a 43-year-old insulation contractor and vice chairman of the Nassau Democratic organization, was designated last Monday by the party's county committee to challenge County Executive Francis T. Purcell. However, Mr. Matthews faces a primary challenge in September from Assemblyman Lewis J. Yevoli, 42, of Old Bethpage, who is accusing his own party leadership of ''an insidious deal'' with Nassau Republicans. The contest, judging by the county committee meeting at the Salisbury Restaurant in Eisenhower Park, shapes up as one between a low-key, relatively inexperienced candidate and an aggressive, street-wise legislator.

The New York Mets lost a 4-2 lead in the eighth, then rallied in the bottom of the inning to score a 7-4 victory over the Los Angeles Dodgers at Shea Stadium yesterday afternoon. The Mets got four runs in the first two innings and entered the eighth with a seemingly safe edge. But Pedro Guerrero tied the game with a two-run home run off Neil Allen, the third of four Met pitchers. The homer was Guerrero's second of the game and fifth of the year.

Mr. Reagan's Tax Problem As the May 15 deadline for a joint budget resolution nears, support for the Administration's tax and budget cutting programs appears strong. However, many Congress-watchers remain convinced that compromise is inevitable when individual committees begin to pare their own budgets next month. Although last week's vote on the House budget proposal gave the White House a stunning victory, some economists say the Administration needs even more firepower. In light of recent indications of unexpectedly fast growth and rapidly decelerating inflation the President's program could use signs of renewed economic weakness in order to convince Congress the nation needs the Reagan tax cut program.

DEMOCRATS say they have more fun than anybody, and that seemed true enough last weekend at their annual fund-raising dinner at the Rye Town Hilton. But they are also more likely to encounter the unexpected, and that also was evident. The 600 guests, who paid $90 a plate, danced through much of the evening, heard appeals from politicians running for office, shared the jokes and nostalgia of such occasions - and then were lambasted by one of their honored guests, May Morgan Robinson, for failing to share political power with blacks. It began auspiciously enough with Representative Peter Peyser of Irvington, singing ''Pennies From Heaven'' and receiving enough applause for an encore, ''Carolina in the Morning.''

After less than four months in office, President Reagan has divided and transformed the once-powerful public officials' lobby, which for the last two decades constituted a united coalition in behalf of more Federal funds for a vast array of local governments and agencies in the Federal system. The President has secured support for his budget cuts among important organizations within the lobby, even though the cuts will result in less public services at all levels of government. Where he has not won support he has muted the opposition. His plan to give the states new authority in the use of Federal funds that have gone directly to local governments has renewed a divisive struggle between the states and the cities, which had reconciled their historic antagonisms when both were tapping new sources of Federal money.