When First Lady Rosalynn Carter came courting Virginia votes here this week, she got her warmest reception from the politically minded blacks her husband always has wooed so successfully.

They lined the street to cheer her arrival and jammed 700 strong into a sweltering neighborhood gymnasium where she was scheduled to speak. But when a Norfolk minister tried to lead a heat-weary choir in a welcoming performance of "The Battle Hymn of the Republic," both he and a stage full of Democratic officials stumbled over the words.

The singing, as a result, was a lot like the president's Virginia campaign: faltering despite the best ofintentions.

"He couldn't take Virginia four years ago when he had everything going for him," said one highly placed Democratic state legislator who insisted on anonymity. "I don't see how he can expect to carry it now."

Virginia, with its 14 electoral votes, was the only southern state Jimmy Carter didn't carry in 1976, largely because Northern Virginia preferred the Republican incumbent, Gerald Ford.

The Carter camp, to the surprise of many in the state, is still hoping the prospect of Ronald Reagan will drive Virginia voters to the president. First Chip Carter, the president's son, and now Mrs. Carter have been dispatched to the state to shore up support but the election day outlook is, by most accounts, grim.

"Both the Carter and Reagan staffs classify Virginia as a marginal state, but the Democrats may be giving it more of a priority than the statistics warrant," says Larry Sabato, a government and foreign affairs professor at the University of Virginia and the state's pre-eminent political analyst.

Sabato says Carter's strength and southern connection was "at a peak" four years ago and not likely to do him as much good this time around. "Carter would be hard-pressed to carry Virginia in a two-way race and when you add the John Anderson factor, it doesn't help," he said.

Still, the political scientist concedes, the Democrats are better organized in the state than they were four years ago and Virginia is not as lost to the GOP as, say, Utah. "The only question in Utah is whether Reagan will get 62 or 64 per cent of the vote," Sabato said.

Rosalynn Carter, therefore, sprinted through her four-hour appearance in Tidewater Thursday without missing a single chance to provide not-so-subtle contrasts between her husband and his chief rival.

"We need you," she told her all-black audience in Norfolk. "You can help the whole country if you vote, not just your people but the whole country."

Stressing her special regard for the Tidewater area "Jimmy and I lived here the first two years of our marriage and our first son was born at Portsmouth Naval Hospital" -- the First Lady spoke of the "stark differences" between her husband and Reagan. And she was never coy in claiming that "blacks, the elderly and other poor and disadvantaged" have a stake in the election.

"The new leaders of the Republican Party are outside the mainstream of the Republican Party -- they departed radically even from the policies of their predecessors," she said.

In Virginia Beach, a half hour's motorcade away, she told a much smaller group of affluent whites that their choice on election day "will determine our future for years to come, not just the next four years." Carter, she promised, would keep the nation strong -- and at peace.

Mrs. Carter, who was accompanied on her Virginia rounds by Lt. Gov. Charles S. Robb, state party chairman Richard L. Davis and other Democratic officials, also tried to turn the tables on Reagan by admitting her husband's own hard times in office.

"When we first came to Washington, we were outsiders, and we were full of confidence that we could conquer Washington overnight," she allowed with a smile. "Well, let me tell you, it didn't work that way."

What politicians say hasn't worked here either, however, is the Carter administration's apparent back-of-the-hand treatment to all that the Tidewater area holds dear: its Navy and shipyard-dominated economy.

The recent decision to send yet another Norfolk-based aircraft carrier to Philadelphia for an overhaul has enraged local merchants and other residents who depend on the military for their livelihood. The reaction has been similar to the outcry from federal workers in Northern Virginia who have been threatened by Carter's crackdown on subsidized parking and other actions. b

"If anybody connected with the shipyard wants to vote for Carter, I'd find it unbelievable, says Virginia Beach's popular Sen. Joe A. Canada, a Republican. Norfolk, which has since declined steadily in population, went for Carter four years ago, while Canada's growing district went Republican.

But Carter's people say Reagan is not the sort to inspire confidence in federal workers no matter what their criticisms of the president. "Although they may not be satisfied with what has happened in the last three or four years, Reagan's tentative proposals for cutting back on government services are totally distasteful to these people," said Bill Romjue, Carter's Virginia campaign coordinator.

Carter lost the state by only 23,000 votes last time, and Romjue says it was Gerald Ford's popularity in Fairfax County that cost Democrats the margin they needed for a victory in Virginia. This year, he says, it will be different because "Reagan is totally out of synch with that area."

Sabato agrees. The federal government work force in Northern Virginia is unhappy with Carter's performance but also concerned about Reagan's "promise," he said. But this situation, he cautions, could wind up benefiting Anderson's independent candidacy.

Carter needs Northern Virginia votes to take the state, and his advisers say the Virginia campaign will pour most of its resources into the region. In fact, the Democratic and GOP tug-of-war over the area is well under way.

"We can't and we won't let Reagan happen to our country," Dottie Schick, the Fairfax County's Democratic chair, proclaimed in a recent mailing to party activists.

She said she had just received some GOP campaign literature at her house and reproduced it in hopes that Democrats would react as she did, with "anger, nausea and an even stronger commitment" to work for Democratic candidates.

The literature, an "Americans for Reagan" letter signed by Sen. Jessee Helms (R-N.C.), called on voters to halt "four more years of Jimmy Carter and his ultra-liberal advisers." With Reagan's candidacy, Helms wrote, "God may be giving us just one more chance to save America."