He is battling with Howard Baker for third place and with Ted Kennedy and Jerry Brown for support among independent voters.

Some say he is likely to wind up as president, but of Common Cause rather than the United States of America.

He is John B. Anderson, a serious person who is trying to convince the voters of New Hampshire that he also is a serious candidate.

"What's the difference between Tweedledum and Tweedledee?" thunders the white-haired Illinois Republican congressman. "What's the difference between George Bush and Ronald Reagan? Bush says there isn't any major difference that he knows of and I believe him."

While talking about Bush and Reagan, Anderson is taking dead aim at Baker, the third-place Republican finisher in Iowa who is assumed to be running third again in New Hampshire.

Anderson believes he can upset that expectation. He is pursuing a longshot strategy which calls for him to finish third ahead of Baker in the New Hampshire primary Feb. 26 and use that as a springboard to a second-place finish behind Bush in the Massachusetts primary a week later.

If Anderson can accomplish this -- and his own poll shows him running second in Massachusetts (with 30 percent undecided) -- he thinks he can become competitive for first place in his home state Illinois primary March 18 and the crossover Wisconsin primary April 1.

The New Hampshire primary could best be described as semi-closed. Independents can vote in the GOP primary, but only if they are willing to become registered as Republicans.

Elizabeth Hager, a former state legislator who is chairman of the Anderson campaign here, doubts that many independents will vote in the Republican primary. She says those who do will vote for Anderson but predicts that most of the independents who participate in the primary will do so as Democrats for Kennedy.

So, the Anderson campaign in New Hampshire is targeting the pockets of progressive Republicans in such communities as Hanover, Lebanon, Concord, Keene and Portsmouth. In Massachusetts there is more emphasis on independent voters, as evidenced by Anderson's campaigning on college campuses and before such liberal groups as the Americans for Democratic Action.

There is some history on Anderson's side in New Hampshire, despite the generally conservative tenor of Republicans there.

California Rep. Paul N. (Pete) McCloskey Jr. received 20 percent of the vote in 1972 while running against then-president Nixon. The same year, Malcolm McLane, then mayor of Concord and now a staunch Anderson supporter, reached the 20 percent figure in a race for governor.

But there are those who say the Republican Party has become much more conservative in the intervening eight years. Even if it is not, some liberals support Bush on the theory that a vote for Anderson is a vote for Reagan.

"What we're really up against is a mood that this has somehow narrowed down to two candidates," Hager says.

Anderson received a blow earlier this week when Bush and Reagan agreed to meet Feb. 23 in a debate sponsored by the Nashua Telegraph. Announcement of this confrontation reinforced the impression that the GOP primary has become a two-person race.

All seven GOP candidates are scheduled to participate in a debate Feb. 20 in Manchester.

As yet, there are scant signs that Anderson is breaking through in New Hampshire. One of his two events Tuesday evening was canceled by a mild flu epidemic at a Manchester school.

The other, at an American Legion hall in Hudson, attracted 38 people, including five reporters, a wire service photographer, four youthful Anderson volunteers from Connecticut, at least three Democrats who said they were for Kennedy, two Republican officials who come out for every candidate and the Reagon town chairman.

Today, only 20 persons showed up for a reception at the Unitarian Church in Milford.

Anderson seems undiscouraged by his uphill fight. He answers every question in eloquent detail, expounding on his favorite proposal for a 50-cent-a-gallon gasoline tax or denouncing the war fever he says the Carter administration has created for political purposes.

His aides are unfailingly courteous and optimistic, recognizing that Anderson has a long way to go but saying it is worth going with him.

"People would say to me when we started, 'Why don't you go for Bush or Baker because they can win?'" Hager says. "It was hard for me to say then that I was for John Anderson because I believed in him. It's easy to say it now."