Virginia Block, a keypunch operator at the Giant Food warehouse in Landover, was going about her business yesterday when Maryland's Democratic Senator, Paul Sarbanes, walked up and grabbed her hand. Before she knew it, she had promised her vote to President Carter.

"It's not every day you get to hold hands with a senator," she explained.

Or, Block might have added, accept a button from a governor, a wink from the state comptroller, and good wishes from a member of Congress -- all in half the time of a coffee break.

Around the beltway yesterday, in offices, senior citizens homes and Metro stations, hundreds of Maryland voters got the same kind of lavish attention from the state's leading Democratic officeholders. Figuring that one old-fashioned bandwagon would draw more attention than isolated stumping, Sarbanes joined by Gov. Harry Hughes, Attorney General Stephen Sachs and other state officials ganged up to tour the state for the Democratic ticket, beginning with Carter.

The two-day road show, which carried the group through Western Maryland and Baltimore's northern suburbs Wednesday, represented the best resource that the relatively improverished and somewhat rudderless state Democratic party can offer the Carter campaign this fall: the words and hands of its elected officials.

Outdone by the state Republican party in fund-raising and field organization, the Democrats nevertheless are capable of reaching and maybe swaying just as many votes as the GOP by simply having their name leaders hit the political club and Metro-stop circuit.

"Politics is theater," said Sachs, whose lukewarm taste for both Carter and Prince George's campaigning left him in a whimsical mood outside of the New Carrollton Metro station. "There's a TV camera here, and people out there will see a senator they respect out campaigning early in the morning, and be impressed."

"It's the perfect way to kick enthusiasm into a campaign," added Ed Crawford, who organized the tour for the Carter campaign. "In Western Maryland, these people have never seen all these guys like Hughes and Sachs at one time before. They're beside themselves."

Even in suburban Washington, the combination of Hughes, Sarbanes, Sachs, Lt. Gov. Samuel Bogley, state Comptroller Louis Goldstein and Rep. Gladys Spellman drew a nest of cameras to a morning press conference, where Hughes announced that he was "scared to death" at the prospect of a Ronald Reagan presidency.

State Sen. Edward T. Conroy, who accompanied the tour of Prince George's yesterday morning, also had a chance to get some much-needed exposure for his charge that Charles Mc. Mathias, the entrenched Republican incumbant he is opposing for the U.S. Senate, did not show up for enough attendance calls on the Senate floor.

By yesterday afternoon, the hoopla raised by the Democratic entourage was making state Republican chairman Allan Levey uncomfortable. "As a matter of a fact," Levey said, "we are planning our own tour of elected officials next week."

"We had been talking about doing it." Levey said, "but after seeing that the Democrats were doing it, we felt we owed it to Mr. Reagan to do the same type of thing." The GOP tour, however, will not feature the one Republican officeholder who might draw the kind of attention the Hughes bandwagon found: Mathias, who is reluctant to be connected to Reagan. "We are not going to bother the people who are campaigning themselves," was the explanation Levey offered.

Of course, a parade of officialdom does not impress many people. One worker at the Giant food plant, his lunch disrupted by a series of speeches from the Democrats, marched out of the cafeteria saying, "I don't have to listen to this. I don't care who they want me to vote for. Anyway, they'll be back in four years."

Even the enthusiasm of some of the campaigners flagged at times. After standing uncomfortably around the entrance to the New Carrollton Metro stop while her colleagues shook hands, Spellman first tried to move to a different spot at the station to campaign, then abandoned the effort all together. "I'm sorry," she said as she departed, "I just can't do this to people."

Sachs, who told reporters that "the Republican party nominated the one person who Jimmy Carter could beat," left after the day's first two events. "The Baltimore Sun said I have a 'what am I doing here look,'" he noted, pinching his face as if to keep it in line. "These other guys get vacations to campaign -- I've got a law office to run."

Hughes, meanwhile, struggled with a cold that occasionally made his voice rasp as he denounced Reagan. "When you are president of the United States you have to be awful deliberate about your decisions and what you say," said the man whose methodical consideration of statehouse matters frequently has exasperated more volatile legislators. "Reagan does not have the reliability and steadiness that we need in the White House."

At 4:30 p.m., the group headed for the Silver Spring Metro station, where, in addition to shaking hands, they did some politicking among themselves.

"Those are people over there waiting for our local buses," Montgomery County Executive Charles Gilchrist said to Goldstein, pointing to a bus marked "Ride-On." "We could use some more money for it."

Goldstein laughed off Gilchrist's suggestion. "Well," he said, "Everyone wants more money."