The Sierra Club and other environmentalists carried their campaign against Interior Secretary James G. Watt to the steps of Congress yesterday--and promised to take their anti-Watt crusade into next year's congressional election campaigns as well.

The environmentalists presented Congress with petitions bearing 1.1 million signatures demanding the firing of the controversial secretary of interior. The petitions were accepted, in a sparsely attended ceremony on the House steps, by House Majority Leader Thomas P. O'Neill Jr. (D-Mass.) and Sen. Alan Cranston (D-Calif.).

The presentation culminated a campaign that began last spring in California. Representatives of environmentalist groups from 46 states presented the petitions before lobbying their own congressional delegations.

Watt supporters have tried to take the edge off the environmentalists' show by putting it down as an attempt to manipulate the media.

On the Senate floor Friday, two Watt supporters, Ted Stevens (R-Alaska) and Strom Thurmond (R-S.C.) denounced "environmental extremists" and attacked the Sierra Club for attempting to stage a "media blitz."

Other Watt supporters leaked a "confidential" Sierra Club planning document outlining a major effort "to achieve maximum political and media impact" through the petition presentation and meetings with the Congress and press.

Watt was out of town on a Republican fund-raising trip yesterday. His spokesman, Doug Baldwin, said before the rally that Watt "thinks the press senses it is being used." Baldwin criticized the Sierra Club action as "a '60s-type Vietnam demonstration, with 50 kids made to look like thousands."

The environmentalists played to a small crowd on Capitol Hill, with their band of petition carriers and the press outnumbering the rest of the rally. But O'Neill, looking down at the mound of signatures, told the volunteers the petitions would have an impact on both Congress and the Reagan administration.

Cranston, who voted against Watt's confirmation and called for his firing last spring, called the secretary "a puppet of the destroyers and exploiters." Watt's policies are "reckless and irresponsible," Cranston said, adding: "I say James Watt must go."

Joseph Fontaine, Sierra Club president, told the rally that the 1.1 million signatures represented "the largest citizens' petition ever presented to the Congress." He said the signatures "demonstrate unmistakably that the American people are opposed to the anti-environmental, anti-conservation policies of the Reagan administration."

Both Fontaine and Rafe Pomerance, president of Friends of the Earth, said the environmentalists would move strongly into the 1982 congressional campaigns, targeting some congressmen for support and also compiling a "hit list" of congressmen to oppose.

The environmental movement has focused its strength on lobbying, rather than elections, in the past. But the League of Conservation Voters, the political arm of the environmentalists, said it planned to spend at least $1 million to mobilize "the green vote" in the 1982 congressional elections.