First Lady Rosalynn Carter left the White House last night to barnstorm Northern Virginia where she told audiences in Alexandria and Arlington and Fairfax counties that her husband needs four more years to win the war on inflation and turn hard times into happy ones.

"We have not had a two-term president since Eisenhower," said Mrs. Carter at each of her brief campaign stops before mostly dedicated Democrats. "How can you solve the long-term problems of the country when you start over again with new peole and new programs every four years?"

Mrs. Carter has made half a dozen campaign appearances during the last two months in Virginia, a state Carter officials apparently now think is winnable.

"The Carter campaign is after Virginia and Northern Virginia is the key," said Jack Sweeney, an aide to Rep. Herb Harris (D-Va.), who represents Virginia's 8th Congressional District.

Some Democrats, however, wondered why Carter officials waited so long to focus more attention on Virginia. And a few, like Richard Barton, were pessimistic about Carter's Virginia prospects, despite Mrs. Carter's recent appearances.

"I think it's an awful long shot that Carter can carry Virginia," said Barton, chairman of Arlington's Democratic campaign committee, who was one of 100 persons at Fairlington Elementary School last night. "I personally feel the Democrats are in worse shape than they were four years ago."

Virginia was the only Southern state Carter did not carry in 1976. But many of the people who saw Mrs. Carter last night said they came for the glamor and weren't that worried about the odds.

"It was tough for Truman also," said Gertrude Greisman, who says she shook Eleanor Roosevelt's hand 40 years ago at the White House. Last night she was content to stand in the rear of the audience at Fairlington to observe and listen to Mrs. Carter who shared the stage with Lynda Johnson Robb, the daughter of the late president Lyndon Johnson and the wife of Virginia's Democratic Lt. Gov. Charles Robb.

Mrs. Carter spoke for 15 minutes during which she described her husband's job as lonely and said the president is "wiser than he was four years ago." In an oblique reference to Ronald Reagan, she also said, "there is no room in the Oval Office for excesses or extremes."

At each of Mrs. Carter's three stops, she spent approximately 20 minutes shaking hands.