PHOENIX, NOV. 2 -- An exuberant, chanting crowd of Arizonans marched into the copper-domed state capitol here today to deliver what they claimed were 390,000 signatures demanding recall of the state's conservative Republican governor, Evan Mecham.

The petitions filed today could lead to a recall election next spring. But the embattled Mecham, who won the governorship last fall with 40 percent of the vote in a three-way race, faces more immediate problems than that.

On Tuesday he is scheduled to testify before a state grand jury on charges that he violated campaign finance laws when he won the governorship. Later this week he is to meet with legislative leaders who are contemplating an impeachment case because of the campaign finance problem.

The mounting pressure on the outspoken 63-year-old governor has created an aura here reminiscent of the atmosphere in Washington during President Richard M. Nixon's final days in the White House. While Mecham and his aides vow that he'll never stop fighting, more and more of his erstwhile allies are urging him to resign from office for the good of the state and the Republican Party.

Mecham has spent his whole political life battling the establishment, including the leadership of his own party; he says his fight to retain office now will be his greatest battle. He has the fervent backing of a bloc of voters who support his strongly conservative brand of Republicanism, but opinion polls show his standing with the general public fading fast.

His bitter public arguments with blacks, feminists, the news media and others have set back the Arizona GOP, a fast-growing party that passed the Democrats in voter registration totals last fall for the first time in the state's history. Recent figures show the Democrats catching up again in voter registration, and the Republican Party here is badly split between Mecham backers and those who want the governor to step down.

The recall drive has also brought forward a most unlikely new face in Republican politics. The man of the hour is 33-year-old Ed Buck, a slender, long-haired businessman who acknowledges that he is homosexual.

Buck started the recall effort last January with two dozen bumper stickers and a handwritten press release. Today, as he triumphantly led the recall activists into the capitol, he was one of the best-known political figures in the state.

Buck's sexual orientation became known early in the recall drive, and Mecham wasted no time blasting his opponents as "homosexual activists." But Buck's frank, articulate responses to this tactic -- "Yes, I'm homosexual," he said. "So what?" -- won him such respect that it is now fairly common to see bankers and lawyers in downtown Phoenix wearing pink lapel buttons that say "heterosexual activist."

Mecham, a millionaire Pontiac dealer who won the governorship on his fifth attempt, got into hot water almost immediately after taking office when he canceled a state holiday honoring the Rev. Martin Luther King Jr.

But the angry protests against that decision were just the prelude to many more contentious battles over Mecham's policies, appointments, and off-the-cuff comments. Republican leaders have repeatedly asked him to try to make peace with his various political enemies, but that runs counter to Mecham's style.

Still, a successful recall seemed unlikely when Buck started his effort. For most of the spring and summer, polls showed that a majority of Arizonans felt Mecham should be allowed to serve out his four-year term.

The tide started to turn this fall, though, when Mecham went on the warpath against his critics. A pro-Mecham bumper sticker aimed at Buck's sexual orientation -- "Queer Ed Buck's Recall" -- caused an anti-Mecham backlash. After Mecham sent out a letter asking conservatives in other states to move to Arizona to support him, polls showed a majority wanted him out of office.

It will take 217,000 valid signatures to force a recall election. Buck said today he gathered 388,989 names, and expressed confidence that more than enough will survive legal challenges to force an election.

If the secretary of state validates 217,000 of the signatures, she will inform Mecham next January. He will then have five days to resign; if he doesn't, an election will be held in April or May. Mecham would then be on the ballot automatically. At least one Democrat will likely challenge him, and it is quite possible that another Republican might enter the contest as well. Current opinion polls suggest that Mecham would lose a two-way contest, but might win if more than one opponent was on the ballot against him.

Meanwhile, Mecham is in legal difficulty because of a $350,000 loan he received from a Phoenix land developer in the closing stages of the 1986 campaign. State law requires disclosure of all campaign loans. Mecham failed to disclose the transaction, and indeed promised the lender in writing that he would keep the loan secret.

After the undisclosed loan became public last month, the state attorney general, Republican Bob Corbin, convened a grand jury to determine if Mecham should be indicted. Mecham initially challenged the proceeding, saying Corbin could not fairly handle the case because he might be a candidate for governor if Mecham were forced out. Today, Mecham's office said he would appear before the grand jury to answer questions.

Mecham says the loan transaction was structured to comport with state law. Still, Republican leaders in the state legislature have hired a special counsel to determine whether the governor should be impeached.

A member of the legislative leadership staff speculated that the impeachment investigation might be just a lever the Republican leadership hopes to use to persuade Mecham to resign.