WASHINGTON — President Donald Trump offered to name Judge Amy Coney Barrett his Supreme Court nominee more than a week ago at the White House — and she accepted, according to formal paperwork submitted to the Senate ahead of her confirmation hearings.

Barrett tells the Senate Judiciary Committee that the White House initially contacted her Sept. 19, the day after Justice Ruth Bader Ginsburg died, creating the court vacancy. Trump made the offer when she visited the White House on Monday, Sept. 21, “and I accepted,” she wrote.

That's days before Trump's formal announcement Saturday, and as he kept Americans guessing up until the last moment, suggesting he was still considering other nominees.

The judge's nearly 70-page questionnaire was submitted by the White House to the Senate Tuesday as Barrett launched day one of private meetings at the Capitol, drawing praise from GOP senators but opposition from Democrats objecting to her conservative views and fast-track confirmation before the Nov. 3 election.

Senate Majority Leader Mitch McConnell said he was “even more convinced” of Barrett after their brief meeting. Noting she is a working mother of seven children, he scoffed at Democratic objections that the judge would put Americans' access to health care at risk or turn back the clock on women's rights. “What a joke,” he said.

As questions swirl about the potential for the results of the presidential election between Trump and Democrat Joe Biden to wind up in a court battle, Barrett offered no suggestion she would recuse herself from hearing any such election cases.

Instead, she said she would recuse herself in matters involving her husband and family members, and her alma mater Notre Dame University.

Leading Democrats say Barrett should not hear any cases about the presidential election because her nomination is the first in U.S. to come so close to one, with early voting underway. But Republicans said Barrett, if confirmed, should absolutely be involved.

Sen. Ted Cruz, R-Texas, said that's “the entire reason” why the Senate should rush to fill the vacant seat — "so that the Supreme Court can resolve any cases that arise in the wake of the election.”

Democrats are confronting the limits of their power as they fight against the nomination. Some have said they won’t meet with Barrett, who is expected to be confirmed for the seat held by the Ginsburg by the end of October. No Democrats met with her Tuesday.

Ginsburg, who died Aug. 18 at the age of 87, was buried Tuesday in a private service at Arlington National Cemetery.

With Republicans holding a 53-47 Senate majority, and just two GOP senators opposing a quick vote, Barrett appears to have enough support for confirmation. The Senate Judiciary Committee released her formal questionnaire, nearly 70 pages, ahead of hearings Oct. 12.

Senate Democratic leader Chuck Schumer acknowledged Tuesday it will be an “uphill fight” to stop Trump’s nominee. But he said Americans are on Democrats’ side in preferring to wait until after the election so the winner can choose the next justice. He is among those refusing to meet with Barrett, calling the process “illegitimate,” and said her conservative views on health care, abortion and other issues are “far outside” the mainstream.

“It’s not over,” Schumer said on ABC’s “The View.”

Barrett made no public remarks at the start of what is expected to be days of meet-and-greet sessions with senators, a traditional part of the confirmation process.

According to a national poll by The New York Times and Siena College that was released Sunday, a clear majority — 56% — of voters believe the winner of the Nov. 3 presidential election should fill Ginsburg’s seat, versus 41% who said Trump should, as the current president.

At the Capitol, Vice President Mike Pence said Barrett “represents the best of America.” The White House formally submitted the nomination Tuesday.

“She’s got a good chance of getting my vote,” said Sen. Chuck Grassley, R-Iowa, the former Judiciary Committee chairman who now helms the Finance Committee.

Ahead of one meeting, Sen. John Thune, R-S.D., the GOP whip, said the two were set “to talk about judicial philosophy and background and experience, and also whether or not she thinks ‘Hoosiers’ is the greatest movie ever.”

The chairman of the Senate Judiciary Committee, Sen. Lindsey Graham, said that barring any unusual developments, “I’m going to vote for her.”

Unable to block Trump’s pick on their own, Democrats are arguing to voters that Barrett’s nomination threatens the protections of the Affordable Care Act — a focus Biden has embraced and many Democrats see as a winning message. The court will hear a case challenging the constitutionality of President Barack Obama's health care law just after the election, adding to the urgency of the issue.

But there will also be ample opportunities for Democrats to make mistakes as partisans on both sides infuse the nomination battle with cultural, gender and religious politics.

Religion, in particular, could be a minefield.

Democrats worry that Barrett has tied her Catholicism too closely to some of her statements and decisions, and California Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, still faces criticism for her comments during Barrett’s 2017 confirmation hearing. Feinstein had joined Republicans on the panel in asking Barrett about her faith, but then went further by telling the then-professor that “when you read your speeches, the conclusion one draws is that the dogma lives loudly within you.”

Some in the left wing of the Democratic Party are pushing for senators to boycott the hearings or commit to adding more justices to the court if Biden wins the presidential election.

For now, Democrats see health care as the perfect counter to Republican hopes that Barrett’s confirmation will bolster Trump’s reelection. More Americans favor the ACA than have opposed it over the last few years, according to polls, and Democrats believe the coronavirus pandemic will only solidify that support. They intend to model their strategy on their successful 2017 fight against Trump and congressional Republicans who tried and failed to repeal the legislation.

One likely prominent messenger on the issue is the Democratic vice presidential nominee, California Sen. Kamala Harris, who sits on the judiciary panel and is expected to participate in the confirmation hearings.

Associated Press writers Bill Barrow in Atlanta, Kathleen Ronayne in Raleigh, N.C., and Emily Swanson in Washington contributed to this report.