Reports of a late swing in voter sentiment have encouraged Republican hopes of turning a predicted Democratic sweep of today's New Jersey and Virginia gubernatorial elections into a double GOP victory that could be read as a voter endorsement of the record of the Reagan administration.

Weekend newspaper polls in both states unanimously showed narrow leads for the Democratic contenders, Rep. James J. Florio of New Jersey and Lt. Gov. Charles S. Robb in Virginia.

But the Eagleton Institute of Rutgers University reported yesterday that callbacks to undecided and wavering voters Sunday found "a great deal of movement" to former New Jersey Assembly speaker Thomas H. Kean, the Republican nominee. "It's very easy to see Tom Kean being elected," said poll director Cliff Zukin, "but Florio could still squeak it out."

An ABC News poll over the weekend showed the race a virtual dead heat among the most likely voters.

In Virginia, Republicans claimed that the weekend canvassing showed evidence of a similar surge for Attorney General J. Marshall Coleman that could push him past Robb, who has led in every public poll since the race began.

In both states, the polls indicated that a heavy turnout in minority areas could carry the Democrats to victory, but GOP National Chairman Richard Richards said, "We have every expectation of celebrating double victories" on the eve of the anniversary of Reagan's election.

The president made campaign appearances for both Coleman and Kean and both have made extensive use of TV commercials in which he endorsed them. The Republican National Committee poured more than $1.2 million into the two states, almost six times as much as the national Democratic party.

To some extent, the Reagan economic program became an issue in both states.

Florio attacked Reagan's budget cuts and said Kean's plan to trim state levies would further cripple needed programs. Robb tried to minimize his differences with Reagan, but Coleman linked himself closely to Reagan's conservative philosophy while portraying Robb as a follower of his father-in-law, Lyndon B. Johnson.

Reagan carried both states in 1980, but otherwise, their political history is a study in contrasts. Coleman is seeking to become the fourth successive Republican governor of Virginia, while Florio is trying to extend the Democrats' domination in Trenton, where they have occupied the governor's office for 16 of the last 20 years.

The New Jersey and Virginia governorships command most attention in the off-year voting that involves legislatures in those two states and Kentucky, mayoral races in a dozen major cities and scattered referenda on everything from nuclear power to budget priorities.

Among the city hall incumbents favored for re-election are Edward Koch of New York, Coleman Young of Detroit, George Voinovich of Cleveland, Donald M. Fraser of Minneapolis, Charles Royer of Seattle, Richard Caliguiri of Pittsburgh and Margaret Hance of Phoenix. All but Voinovich and Hance are Democrats, but Koch has received the GOP nomination along with that of his own party.

In Houston, Mayor Jim McConn has been lagging in polls behind challengers Kathy Whitmire and Jack Heard. A runoff will be held Nov. 17 if no one in the 15-person field receives a majority.

In Miami, Mayor Maurice Ferre, the first native of Puerto Rico to win a big city mayorship, faces a serious challenge from Cuban-born Manolo Reboso.

Among the referenda on the ballot will be a Washington state nuclear power issue, a Boston advisory vote on giving domestic programs priority over military weapons, a Kentucky vote on allowing the governor two successive terms, and an Ohio vote on taking redistricting away from a Democratic-dominated board and giving it to a bipartisan body.