When three dozen House Democrats met last Firday to plot strategy for an open convention, they decided it would show their broad base of support if a younger member acted as a spokesman along with nine-term Rep. Don Edwards of California.

"So we looked around the room," recalled Rep. James A. Ambro (D-N.Y.), "and there was Mike."

Rep. Michael D. Barnes (D-Md.) insists that "I didn't hold up my hand," but he quickly accepted the assignment, and in less than a week it propelled him from the relative obscurity of a freshman legislator from surburban Montgomery County to the national spotlight.

It is too soon to tell what impact Barnes' sudden celebrity will have on his own future. He contends he hasn't jumped on the dump-Carter bandwagon for personal political gain.

But the 36-year-old lawyer is locked in a bitter re-election campaign against Newton I. Steers, the Republican he narrowly unseated two years ago. And Barnes' own poll shows that Carter is running "a poor third" in his 8th Congressional District, behind Republican Ronald Reagan and Independent John Anderson, who are neck-and-neck in the lead.

Steers, for his part, is trying to put the best possible light on Barnes' new role, predicting it will backfire by protraying Barnes as a back-stabbing, unethical opportunist.

As a spokesman for the open convention movement, Barnes has appeared on talk shows and network newscasts, had his picture displayed in newspapers across the land, and been interviewed by the news magazines.

In an attempt to offset the free publicity Barnes is getting, his millionaire challenger is going to buy some publicity of his own this weekend.

Steers is spending $12,000 on hastily recorded radio and television commercials that will be broadcast beginning today. The 30-second spots denounce Barnes for being "ethicallly inconsistent." They note that Barnes supported the Carter administration 30 percent of the time, but say "now that he thinks Carter is a loser he's crying for a new presidential candidate . . . "That's politics for politics' sake, and it's what's wrong with Congress today."

Interviewed at a $150-a-person fund-raising event at the home of House Minority Leader John Rhodes (R-Aria.), Steers and Barnes' action is "the best news I've had in a long time. He understandably wants to leave a sinking ship, but I am going to make it as difficult as possible for him because he was one of its designers."

Steers' campaign manager, Jeanne Miller, predicted, "Barnes is going to lose votes on this."

Maryland State Sen. Howard Denis, who is Steers' campaign chairman, was more cautious, calling Barnes' move "a risk for us, and an opportunity for us."

Whatever the outcome, Barnes was clearly in the right place at the right time.

The biggest stroke of luck came last Satruday morning, when Bill Monroe, moderator and executive producer of NBC's "Meet the Press," decided to scrap the next morning's previously taped interview show (a climatalogist talking about the heat wave) in favor of the open convention movement.

"I was spending the day in a country cabin," Monroe explained, "and didn't have a phone book. I saw the names of the leaders (of the movement) in the newspaper, and attempted to reach them. I called information, and the operator said Mike Barnes was listed in Kinsington. He was in the book."

And that was it. Barnes answered the telephone and quickly agreed to appear as the guest on the program, a sure-fire method of winning national exposure. (Monroe also later reached Rep. Edwards, who declined to appear.)

Barnes, a quiet, studious type, admits that after a week in the spotlight, "when I am alone with my wife or friends, I say, 'This is obviously not happening to me.' The media part seems very unreal, as if it is happening to someone else. If I had been told a week ago, 'You are going to be on Meet the Press,' I would have said, 'Sure, and my wife is the queen of England.'"

The open convention idea was a natural for Barnes, who steadfastly refused to endorse either Carter or Sen. Edward M. Kennedy, often telling associates that he would like to see his former boss, Secretary of State Edmund Muskie, nominated and elected president.

"We're not talking about saving our rear ends," said Barnes. "It may sound corny, but we're interested in saving the Democratic Party and the country."

Responds Steers' supporter Denis: "Barnes' action reflects panic, inexperience and an inability to rise above politics. It's not like the Gene McCarthy movment (of 1963). These guys have no candidate, no philosophy and their only issue is to save their ass."

As for Barnes' celebrity, Denis said, "It's a heady wine now, but as with all other intoxicating beverages, there will be a morning after."

On that, Barnes agrees. "Andy Warhol says everyone in the world should be given five minutes of fame. Well, I've been given mine. Two weeks from now, I'll be back representing Montgomery County."