When the Reagan administration asked Anne McGill Gorsuch to consider taking a job in Washington, running the Environmental Protection Agency was not what she considered first.

"I gave it a lot of thought," she said. "What's the toughest job in town? David Stockman had it. The EPA was next."

Gorsuch, 39, didn't go after the Office of Management and Budget job but went after her No. 2 choice -- and got it. She took over as EPA administrator on May 20, and from the moment she was nominated critics questioned her commitment to the environment.

They have doubted the former state legislator's administrative experience, and they have worried that she might not be independent or crafty enough to survive in the sea of sharks that surrounds EPA. They wanted to know if she was tough enough for what she called the second-toughest job in Washington.

By all accounts. Gorsuch is working nights and weekends to show that she is.

Still without assistant administrators or regional chiefs, she is trying to run her 5,500-worker domain almost singlehandedly. She has frozen contract-letting, canceled all public appearances by staff members and ordered them to stop talking to members of Congress or to Capitol Hill staff people without formal permission.

President Regan cut $400 million from the $1.63 billion that former president Carter budgeted for EPA in 1982, and Gorsuch has proposed cutting $100 million more, half of it from research and development. She has split EPA's enforcement office and put the parts into the air, water, toxic chemical and other program areas, a move that critics say will mean much less enforcement effort. She denies that.

Gorsuch is anything but relaxes. In interviews and meetings she sits all but motionless, her gaze locked on the questioner and her responses short and to the point.

"She asked for our positions and offered absolutely nothing in the way of what she was thinking," summed up Richard Ayres of the Natural Resources Defense Council after a meeting with Gorsuch on revisions to the Clean Air Act. "Anything remotely suggesting she wasn't knowledgeable about some fine point got a rise out of her."

A source who was present when Gorsuch met with members of the National Governors Association and their staffs called her "a little bit combative, mildly confrontational." He said that she was told that most governors do not want the Clean Air Act changed so that pollution limits are set at the state level. a shift Gorsuch reportedly favors, she "was blunt to the point of being rude" in her disagreement.

"She told us we'd be able to support the administration position. I didn't know if she meant we'd love it or that we'd damn well better support it," the source said.

The other side of that coin is a lawyerly attention to detail that kept Gorsuch working late with attorneys in her general counsel's office on the nuances of litigation over a complex part of the Clean Air Act. "That won her the respect of a lot of the staff," said an attorney. "She gets into the meat of the issues and she's a quick study."

She likes to give orders orally, putting little on paper, preferring the give-and-take of a meeting to curculating memos, employes say. They chorus that she is full of sharp questions and remembers the answers.

With the lower paper flow, some career bureaucrats feel left out of the decision-making process. "She talks to very few people outside her aides. She's not using us," complained a staffer in the hazardous waste control section.

But White House officials give her high marks so far. "She's going to set objectives and hold people accountable," one said. "She'll be a hard-line administrator."

Gorsuch is the second-ranking woman in the new administration, after United Nations Ambassador Jeane Kirkpatrick, who has Cabinet status.

yreagan, who campaigned with promises to rein in the EPA, demoted the EPA administrator's job from the Cabinet rank it had under Carter. Gorsuch wants to help make EPA less visible in another way: the impact of its regulations.

Fully half the troublesome regulations that industrial groups spot-lighted for Vice President Bush's regulatory reform team were EPA rules and the delays they involve, Gorsuch asserts. States asking permission to revise the way they implement the Clean Air Act have waited two years or more for approval of minor changes. Businesses wait forever for permit processing.

But she would not discuss proposals to make approvals automatic if EPA fails to act on applications in a limited time.

"The primary job of EPA is to protect the environment, but we have to do taht in a less procedure-oriented mode and a more result-oriented mode," she said. "I don't consider efficiency and environment to be mutually exclusive."

Gorsuch, a native of Casper, Wyo., was a Colorado legislator from 1976 to 1980 while working as a corporate attorney for Mountain Bell Telephone Co. in Denver. She got into public life, she said, out of a desire to "return the investment" that Colorado had made in her education.

"People with different talents serve differently: in Boy Scout troops, at PTA levels, on boards of directors. Through my education and training I really looked forward to public service as an elected official," she said.

She resents the charge that she has no environmental interest and notes that she chaired an interim committee on hazardous waste and wrote the state's program to inspect automobile emissions controls.

"I don't know how much more environmental credentials I need," she said. "The record speaks for itself."

But her critics say this record is not one of environmental activism. They note that Gorsuch's hazardous waste committee voted to oppose any state involvement in the federal program to control wastes. Gorsuch said later that if the feds were going to dictate the outline of the program, it was up to them to run it.

In addition, she offered her bill on inspecting emissions controls only after EPA threatened to shut off Colorado's funding because of its lack of one, a threat she vehemently denounced. In her confirmation hearings, she criticized EPA's fund-cutoff power, saying she would try instead to use incentives to get states to cooperate.

She came to Washington amid speculation over the 2 1/2-month delay in her confirmation proceedings and over her relationship with three other prominent Colorado Republicans: Interior Secretary James G. Watt, Bureau of Land Management chief Robert Burford and beer magnate Joseph Coors.

Coors, a founder of the Mountain States Legal Foundation that Watt headed, joined Watt and Sen. William Armstrong (R-Colo.) in recommending Gorsuch for the EPA slot last January.

Gorsuch said that she knows Coors from working with him to elect Reagan. His only EPA interest would appear to be in the control of brewery wastes, which are regulated like other nontoxic wastes, and in container laws, which are largely state option. Coors' breweries have an excellent reputation among environmental groups.

Gorsuch was romantically linked to Burford in Denver gossip last year, but the gossip is just that, she said -- gossip. "We have a close working and close personal relationship because of a long association while we were both state legislators."

Once Gorsuch arrived in Washington, she holed up in an office down the hall from Watt's at the Interior Department while waiting for security clearance on her nomination. That took a while because of the year she spent as a Fulbright scholar in India, studying the penal system, according to White House officials.

Gorsuch is irritated by efforts to compare her with Watt. While religion is also an "important part" of her life, as it is with Watt, she said, "My private life is my private life. I am not James Watt."

She bridled at environmentalists' worry that Watt would dimonate environmental decision-making and the rewrite of the Clean Air Act because he heads the Cabinet Council on Environment and Natural Resources. b

"The minute I was confirmed I took over the chairmanship of the [Clean Air Act] work group and I have conducted their meetings ever since," she said. She is driving her staff hard to make the June 30 deadline that she promised Congress for the administration position on the act.

As for her critics, Gorsuch is philosophical: "It would be more rational to wait and see what my performance is. I don't operate in terms of what people say about me."