On the morning of the historic day that the House of Representatives voted to hold her in contempt of Congress, Anne McGill Gorsuch was at the dentist. That afternoon, as the White House negotiated with House leaders to try to head off the vote, she attended an office Christmas party.

That night, when the House vote made her the first Cabinet-level official to be held in contempt, she was more than a mile away, watching the proceedings on cable television at the Environmental Protection Agency, where she is administrator.

In many ways, Gorsuch has only a bit part in the constitutional drama unfolding between Congress and the executive branch over her refusal to turn over subpoenaed documents to the House. The EPA administrator acted on orders from President Reagan, who was advised by the Justice Department.

But from her office overlooking Washington's southwest waterfront, Gorsuch saw her role as critical. It is the role she has played since arriving at EPA: good soldier for the president.

Her mission, as she described it in an interview on the day after the House vote, is "to serve this president wherever I can serve him best, as long or as short as he wants me." So, she said, "This is not a bit part at all."

As Reagan's point person at EPA, the former corporate lawyer and Colorado state legislator has spent 19 months, along with combative Interior Secretary James G. Watt, in the eye of the political storm over the Reagan administration's environmental policies.

Behind the desk of Gorsuch, the soldier, hangs a full-color photograph of Reagan and Vice President Bush. On her desk lies a recently published book about Watt, her comrade-in-arms, entitled "At The Eye of the Storm: James Watt and the Environmentalists."

Watt and Gorsuch are friends from their days in Denver, and he wrote in a note attached to the book that he wanted to share it with her "because you and I have been subject to so many abuses and have been able to withstand the onslaught of the enemy."

Both Republicans and Democrats have risen on the floor of Congress to accuse Gorsuch of dismantling her agency rather than directing it aggressively to protect the environment. They point to cuts in budgets for research and enforcement, to steep declines in the number of cases filed against polluters, to efforts to relax portions of the Clean Air Act, to an acceleration of federal approvals for the spraying of restricted pesticides, and more.

Gorsuch, 40, has appeared repeatedly before congressional committees to defend these moves, a striking figure with jet-black hair and a flair for combat that once brought this assessment from a Rocky Mountain News editorial: "She could kick a bear to death with her bare feet."

Gorsuch has responded to critics that EPA budget and staff cuts represent streamlining, not gutting, and that the agency should be judged not on the number of lawsuits it files, but on its accomplishments.

"Have these people ever bothered to look at the facts?" she asked. "It doesn't take much courage to stand up and say Anne Gorsuch isn't doing a good job, but I challenge them to look at the facts."

So many people have stood up and criticized Gorsuch that she and Watt have become political symbols, the stuff of Doonesbury columns and Democratic broadsides. Their names appear regularly in environmentalist fund-raising letters, with lucrative results, according to several direct-mail consultants.

"We lump Gorsuch and Watt togther as symbols of the Reagan administration assault on the environment," said Marion Edey, leader of the nation's largest environmental political action committee, in discussing the 1982 campaign.

Gorsuch, like Watt, has also taken heat from industry spokesmen, who complain that all the controversy has tainted industry's much sought-after "regulatory reform" effort to lessen government restrictions.

After White House polls during the 1982 election campaign showed a growing public perception of the administration as anti-environment, high-ranking aides to the president began to speculate that Gorsuch might soon be out of a job.

But now that the heat is at its most intense, with Gorsuch facing a criminal contempt of Congress charge, her job security appears to have improved immensely. "Whatever else was going on before, I'm sure that's all frozen in place for at least as long as this case goes on," said an administration official close to the issue. To replace her now would look like a retreat, he added.

In Congress, where Gorsuch was often characterized by critics as the "Ice Queen" because of her tough exterior, she has been recast by many House members in the ringing debates of the past few weeks as a cross between a helpless victim and a near-saint.

"I speak with some degree of concern and sympathy," Rep. Marc L. Marks (R-Pa.) said to Gorsuch during a subcommittee hearing on the contempt citation. "Seeing Mrs. Gorsuch sitting there all by herself, one must feel a bit sorry. She has so many things to do, and I might add is doing them quite well, to put her through this."

Even as the House was voting to find her in contempt, members rose to characterize Gorsuch as "a very fine lady" and a "woman who has worked hard to serve her country."

This was part of an effort, according to several congressmen, to clarify that the contempt citation was aimed not at Gorsuch, the soldier, but at the Reagan administration, for what Marks called "shocking" efforts to withhold information from Congress. In fact, Marks pointed out, Gorsuch and her staff originally allowed House subcommittee staff members to read some of the sensitive legal documents now being withheld under Reagan's claim of executive privilege.

The documents, which pertain to potential prosecution of major companies for illegal hazardous waste dumping, were declared off-limits after the Justice Department reviewed the matter, Gorsuch confirmed. Reagan, acting on advice from Justice, instructed Gorsuch to withhold the documents, saying they contained information that, if released, could jeopardize cases against the firms.

"I find it almost shocking that both the majority and minority staff have had access to these documents in the past," Marks said, "and still, the attorney general says the president can invoke executive privilege" to keep them from Congress.

The constitutional showdown has escalated from day to day. After both Republicans and Democrats voted in the House to charge the executive branch with intruding on the rights of Congress, the Justice Department sued the House, charging it with intruding on the prerogatives of the executive branch.

Gorsuch contended she is "not impressed by that kind of stuff." She rolled her eyes, as if to downplay the drama unfolding around her, and quoted something she saw hanging on the wall of Reagan's close friend and adviser, Sen. Paul Laxalt (R-Nev.): "It's amazing how much one person can do so long as they don't care who gets the credit."