Impatient for the election she expects to make her Britain's first woman Prime Minister, Margaret Thatcher goes to the United States next Tuesday for a visit with President Carter and others of power and influence.

"I'm the next government," she cooly observed in a chat with American reporters the other day. "I think I should meet your cabinet."

Her 2 1/2 years as Conservative Party leader have only increased Thatcher's confidence and self-assurance, qualities with which she was already well-endowed.

She has quickly learned that the mighty are not awesome. "You go about and talk to other world leaders," she told an interview last spring, "and you realize that they have no more magic answers than you have."

She has seen and learned nothing to shake her conviction that the good life the moral life, consists of a minimum of state intervention in the economy and a maximum of self-reliance and private enterprise. "It's the vigor, the risk-taking, the energy, the innovation that I admire in American," remarked Thatcher, who has earned the title here of "Iron Butterfly."

She knows that if there were a vote today, a Labor government struggling with high inflation, high unemployment and sluggish output would almost surely be driven from office. But she also knows she is a long step from 10 Downing street because Prime Minister James Callaghan will delay an electon as along as possible, counting on a pump-priming tax cut to revive British fortunes.

"I can't fight the laws of arithmetic," Thatcher said sharply when asked how long she expects to be kept from office. She means that 13 Liberal members of Parliament, even more frightened of an election than Labor is, must be counted in Callaghan's ranks and they keep him in power. somehow, she hopes, the Liberals will break loose. Somehow, she hopes, "10 good men and true" from Callaghan's rightwing will defect.

She tells her own back-bench members of parliament, "I believe in the law of the unexpected, Margaret Thatcher's law of the unexpected in politics." Somewhere, she is convinced, the government will stumble and she will have her chance well before the 1979 deadline when Callaghan must go to the country.

As Tory leader, she has resisted media advice to soften her image as an immaculately groomed, 51-year-old suburban matron with her sensible shoes firmly planted on the right. She has made no concessions to conciliate moderate leaders in her own party. Edward Heath, whom she ousted as leader, and his principal deputy, Peter Walker, are still on the back benches and not in her shadow Cabinet, the key opposition group that advises on policy.

Anything softer than hard line would not be congenial for her. Anyway, she probably knows better than the media that elections turn on the government's performance and not the opposition's style. Her stance, moreover, arouses enthuriasm among Conservative Party workers, a decided plus in any national contest.

The Labor Party has tried to turn Thatcher into an electoral asset of their own, painting her as a scarecrow to frighten trade unions and workers.

She is amused by this. "Well, the idea of me as a bogey is really absolutely absurd," she told an interviewer. "When they try to set me up as that I really think that I must be pretty successful."

Parliament-watchers would give her leadership mixed marks. She has turned up the party machine to a fighting pitch. On the other hand, she has generally come out second to Callaghan in their twice-weekly tiffs at question time.This peculiar ritual has no substantive importance, but the morale of back-benchers rises and falls with the performance of their leaders. Finally, some critics fault her for not winning over the Liberals before Callaghan embraced them.

Thatcher will spend a crowded 10 days in New York, Houston and Washington. But the grocer's daughter who won a scholarship to study chemistry at Oxford and passed her final law exams three months after giving birth to twins has never been charged with lack of energy.

Apart from the president, she is due to see Cabinet Members Cyrus Vance, James Schlesinger, Michael Blumenthal, Burt Lance, Harold Brown and U.S. Ambassador to the United Nations Andrew Young.

She has meetings with editors of virtually the entire East Coast media establishment - The Wall Street Journal, NBC, Time, The New York Times and The Washington Post. She will see banking's top brass, including David Rockefeller, chairman of Chase Manhattan, and Arthur Burns of the Federal Reserve Board. She will mount an oil rig in the Gulf of Mexico, dine with Henry Kissinger and call on George Meany.