Voters go to the polls today in Virginia and the District of Columbia for elections that have national implications.

Virginia is the scene of a gubernatorial contest viewed as a referendum on the Reagan administration and D.C. has an educational tax credit initiative that will be watched closely by school officials across the country.

The acrimonious, expensive gubernatorial race in Virginia, pitting Democrat Charles S. Robb against Republican J. Marshall Coleman, is expected to attract up to 60 percent of the state's 2.2 million voters. Virginians also will pick successors to Robb and Coleman as lieutenant governor and state attorney general, and members of the state House of Delegates.

Election officials in the District of Columbia expect only about 15 percent, or 41,000 voters, to turn out for an off-year election in which voters also will elect five members of the school board, select delegates to a statehood constitutional convention, and choose members of the city's Advisory Neighborhood Commissions.

Forecasts call for temperatures in the 60s and 70s across the state today -- pleasant fall weather that spokesmen for both Robb and Coleman said would not affect the outcome.

Polls are open from 6 a.m. to 7 p.m. in Virginia, and from 7 a.m. to 8 p.m. in D.C.

The only other statewide election today is in New Jersey, where about 60 percent of the state's 3.6 million voters are expected to vote. They will choose between Democrat James Florio, a four-term member of the House of Representatives, and Republican Thomas Kean of Livingston for governor. They also will elect members of the legislature and vote on a record eight ballot questions.

President Reagan has campaigned in both Virginia and New Jersey for the GOP nominees. In Virginia, Coleman has made his ties to the president a cornerstone of his campaign and Robb largely refrained from criticizing the president. In New Jersey, Kean, while stressing his ties to the president, has denied that the vote is a referendum on Reagan policies. Florio has attacked the president's economic programs.

In final campaigning yesterday, both Coleman and Robb predicted victory. "It is going to be very close, but we are going to win," said Robb. "I'm going to come from behind and win," said Coleman.

Robb, 42, the son-in-law of former President Lyndon B. Johnson, will attempt to become the first Democrat to be elected governor in Virginia since 1965, while Coleman, 39, seeks to continue a string of GOP victories in what formerly was a one-party, Democratic state.

The District of Columbia's tax-credit initiative would give up to$1,200 per pupil in D.C. income tax credits to taxpayers for the educational expenses of D.C. students. Interest generated by the question may boost an otherwise low turnout among 273,000 registered voters, according to Lillie Fitzgerald, administrator of the Board of Elections and Ethics.

District of Columbia voters will choose among 29 candidates for five school board seats, two to be chosen at-large and one each from Wards 2, 3 and 8.

Joan S. Mahan, secretary of the State Board of Elections in Richmond, said that, based on absentee balloting, she expects a turnout of between 1.3 and 1.4 million voters. In the last gubernatorial race in 1977, just over 1.2 million persons voted in an election in which Republican John N. Dalton defeated Democrat Henry E. Howell. Last year, 81.4 percent, or about 1.8 million people, voted in the presidential race in which Reagan carried the state 53 percent to 40 percent over incumbent Democrat Jimmy Carter.

Coleman's running mates are State Sen. Nathan H. Miller of Harrisonburg for lieutenant governor and former Del. Wyatt B. Durrette of Fairfax for attorney general. The Robb team includes former Portsmouth mayor Richard J. Davis for lieutenant governor and Del. Gerald L. Baliles of Richmond for attorney general.

In Virginia's legislative races, 148 candidates are vying for 82 contested seats in the 100-member House of Delegates, which Democrats now control 74 to 25, with one independent.

Voters in Arlington and Loudoun counties will be selecting a new member for their county boards. Arlington and Fairfax voters will be deciding the fate of bond issues for jail expansion, roads, and school construction.