Brett Kavanaugh’s nomination to fill a crucial U.S. Supreme Court seat is headed toward a Senate confirmation vote — but how fast it gets there will be determined by whether outnumbered Democrats succeed in a tactic that could postpone a decision until after the midterm elections.

Those elections could maintain Republican control of the Senate, virtually guaranteeing confirmation of Kavanaugh and solidifying conservative control of the high court for years to come.

But if Democrats succeed in both putting off a vote on Kavanaugh and prevailing in an election in which they’re defending more Senate seats than Republicans, the nomination could be in trouble.

The Democrats’ strategy, led by California’s Sen. Dianne Feinstein, is to demand to see every document that crossed Kavanaugh’s desk while he served as President George W. Bush’s staff secretary from 2003 to 2006. Republicans are pushing back, hoping to confirm Kavanaugh, now an appeals court judge, by the time the Supreme Court’s next session starts in October.

“What are Republicans and the White House trying to hide?” asked Feinstein, the top-ranking Democrat on the Senate Judiciary Committee, which will consider President Trump’s nomination of Kavanaugh to succeed retiring Justice Anthony Kennedy. She said the importance of the records in evaluating Kavanaugh is shown by his statements that as staff secretary, he “worked closely with the president and with the senior staff” and was called on by Bush “to provide advice on a full range of subjects.”

Republicans say the only records that are relevant to Kavanaugh’s qualifications are the rulings he has issued in 12 years as an appeals court judge, and possibly documents he wrote as a White House lawyer from 2001 to 2003, but not the voluminous paperwork that crossed his desk in three years as staff secretary. Democrats are playing a “delay game,” said Sen. John Cornyn, R-Texas.

If it’s a game, the majority Republicans hold most of the cards, with the votes to decide what information gets released ahead of the hearing. Whether they have anything to hide is uncertain, but one Democrat finds a clue in the history of a current federal appeals court judge in San Francisco.

In 2003, recalled Sen. Patrick Leahy of Vermont, Bush nominated Justice Department attorney Jay Bybee to the Ninth U.S. Circuit Court of Appeals. Leahy, then the Judiciary Committee’s top Democrat, asked him whether he had dealt with legal issues in the administration’s “war on terror.” He said Bybee did not answer.

A year after he was confirmed by the Senate, Bybee was revealed as the official who had signed off on a 2002 memo drafted by another Justice Department lawyer, John Yoo — now a UC Berkeley law professor — authorizing torturous treatment such as waterboarding for terror suspects in U.S. custody.

“Had we known that at the time, Mr. Bybee would not have become Judge Bybee,” Leahy said in a column in the New York Times.

Because Kavanaugh was “directly involved in some of the most politically charged moments of our recent history,” he wrote, “the Senate owes the American people an unsparing examination of his nomination.”

Another Senate Democrat, Dick Durbin of Illinois, says he’s been waiting more than a decade for Kavanaugh to explain his involvement in Bush administration detention and interrogation policies.

At Kavanaugh’s 2006 confirmation hearing to be appeals court judge, Durbin asked what he knew about another official’s role in those policies. Kavanaugh replied that he was “not involved in the questions about the rules governing detention of combatants.”

That response was misleading, Durbin said at a recent hearing. He cited reports in 2007 by the Washington Post and National Public Radio that Kavanaugh had discussed with other officials the detention of U.S. citizens held as alleged enemy combatants. Kavanaugh reportedly told them that Justice Kennedy, for whom he had clerked, would probably rule that they were entitled to lawyers, contrary to the Bush administration’s position. It proved to be an accurate prediction.

After those reports, Durbin sent Kavanaugh a letter asking about the apparent contradiction and calling on him to disqualify himself from appeals court cases involving detainees. He said he never got an answer.

Democrats aren’t any more likely to get the answers they’re looking for now, said Rory Little, a law professor at UC Hastings in San Francisco and a former Justice Department attorney and Supreme Court law clerk.

Feinstein and her colleagues are making “a very legitimate request” for records of Kavanaugh’s White House years, Little said, but Republicans also have a basis for responding “that this is a fishing expedition and you’re just trying to delay things.”

He said Democrats are clearly hoping to delay a vote on Kavanaugh until after the November elections, when they hope to take control of the Senate. That will be difficult: While Republicans’ current majority is only 51-49, 26 of the 35 seats up for election this year are being defended by Democrats.

Little also recalled the seemingly explosive revelation of Supreme Court nominee William Rehnquist’s writings at his 1971 confirmation hearing. Senators learned that as a Supreme Court law clerk 20 years earlier, Rehnquist had written a memo saying the court’s 1896 ruling upholding racial segregation “was right and should be reaffirmed.”

Asked about the memo, Rehnquist said he had merely been expressing the view of his boss, Justice Robert Jackson. Most historians have rejected that explanation — noting, among other things, Jackson’s participation in the unanimous Brown vs. Board of Education ruling in 1954 that outlawed state-sponsored segregation — but enough members of the Democratic-controlled Senate accepted it to confirm Rehnquist to the court.

Even if Democrats unearthed “a copy of the torture memo with Kavanaugh’s initials on it, indicating it passed through him, would that change people’s votes? I don’t think so,” Little said.

Kavanaugh was screened extensively during his confirmation process as an appeals court judge, and it’s unlikely the Democrats will uncover anything embarrassing now, said Jessica Levinson, who teaches courses in law and politics as a Loyola Law School professor in Los Angeles.

Describing Kavanaugh as very conservative but within the judicial mainstream, she said Democrats lack the votes needed to pry loose any records and must rely on “trying to sway public opinion.”

Little also said a “galvanized grassroots movement” might change the equation. On Thursday, civil rights groups are hoping to initiate such an effort locally at a meeting in Berkeley they’ve labeled #StopKavanaugh (Bay Area).

A similar meeting took place more than 30 years ago to organize local opposition to President Ronald Reagan’s nomination of Robert Bork to the Supreme Court, recalled San Francisco attorney Eva Paterson, president of the Equal Justice Society and organizer of Thursday’s session. “Nobody thought we could stop him,” she said, but the Senate rejected Bork, and Reagan later named the more moderate Kennedy to fill the vacancy.

“This is a 50-state strategy,” said another participant, Leslie Proll, a Washington, D.C., civil rights lawyer and adviser to the NAACP on judicial nominations. She said organizers, who include leaders of feminist and abortion rights groups, want to encourage Californians to support Feinstein’s effort to obtain Kavanaugh’s records, and to “use their networks ... to reach out to their friends, families, colleagues, classmates who live in other states.”

But local action isn’t limited to Kavanaugh’s opponents. The antiabortion group Susan B. Anthony List, which supports the nomination, says nearly 500 of its canvassers have visited more than 1.1 million homes in states including Indiana, Florida, Missouri and North Dakota, where Democratic senators face re-election challenges. Advocates for and against Kavanaugh have also budgeted millions of dollars for television ads, mostly targeting swing states.

There might be one more role for selected members of the public, said UC Hastings’ Little: Democrats who can’t get Kavanaugh’s documents from officials channels are signaling, he said, that they’ll accept them from anyone who has them.

“The fact that this (need for records) has been announced publicly is, in today’s world, an invitation to leak,” he said. The message is, “‘Anybody who has information out there, send it to us.’”

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @BobEgelko