WASHINGTON (Reuters) - When a group of visiting political advisers sought to persuade then-Senator Joe Biden to run for president in 2004, his wife Jill sat poolside at their home, fuming.

Finally, she took action. She drew the word "NO" in ink in large letters on her stomach and "marched through the room in my bikini," she wrote. He decided against running that time around.

The anecdote, laid out by Jill Biden in her 2019 autobiography, "Where the Light Enters: Building a Family, Discovering Myself," makes plain that she hasn't always liked the idea of her husband running for president.

But she later came around to the idea and now, after his stumbling debate performance last week against his Republican rival, Donald Trump, the first lady is instead saying "No" to the idea of Biden pulling out of the race.

Even as some fellow Democrats call on Biden, 81, to accept that he is too old for a second term, Jill Biden appears to be holding firm.

"Joe isn't just the right person for the job," she told donors in East Hampton, New York, on Saturday. "He's the only person for the job."

"She has dug in her heels to support the president. She has been the most ardent and fervent supporter, campaigner, surrogate, defender, and protector than anyone around him, and clearly has tremendous influence," said Anita McBride, who was chief of staff to first lady Laura Bush and co-author of "U.S. First Ladies: Making History and Leaving Legacies."

Married to Jill for 47 years, President Biden is leaning heavily on his 73-year-old wife as he battles to overcome doubts about his mental acuity and ride out the political firestorm over his debate performance.

In "American Woman," a book about first ladies in the modern era, author Katie Rogers wrote that when Biden has a difficult decision to make, he often turns to Jill as his "gut check" and closest confidante.

The first lady, who once physically blocked a protester from the stage in Los Angeles where Biden was speaking in 2020, is not only standing by his side, she is also trying to rally support for him among Democrats.

"Joe, you did such a great job, you answered every question, you knew all the facts," Jill told him at a watch party in Atlanta after the debate, drawing some ridicule on social media.

At a New York fundraiser on Friday night, she recounted one post-debate conversation with Biden.

"'You know, Jill, I don't know what happened. I didn't feel that great.' And I said, 'Look, Joe, we are not going to let 90 minutes define the four years that you've been president,'" she said.

Biden has always kept a tight circle of family members and senior advisers around him. The first lady is a powerful figure in the group but is not a "political decider" and trusts Biden's professional staff, said her former press secretary Michael LaRosa.

Any decision about Biden's future would probably include advice from a mix of top advisers, LaRosa said. "I don't think Jill is going to be comfortable with making that kind of decision."

Jill Biden, a community college educator, is the first presidential spouse to hold down a fulltime job while filling the White House role, which includes an aggressive schedule of official and campaign events.

Trump's wife, Melania, rarely campaigns for him.

"The president has plenty of political and policy advisers - that's never been her role," Elizabeth Alexander, Jill Biden's communications directors, said of her boss.

"As much as any husband and wife team make decisions together that impact their lives, they absolutely do, but as she's said more times than I can count - politics is his lane. She supports his career and he supports hers," she said.

Jill Biden frequently tells audiences that it took her some time to decide to marry then-Senator Biden - after five proposals.

"I knew that whatever I chose my life would change forever," Jill Biden said in East Hampton. "Of course I would no longer be single. But I would become the mom to two young boys, Beau and Hunter, overnight. And becoming a senator's wife would mean a life in the spotlight."

(Reporting By Steve Holland; Editing by Heather Timmons and Howard Goller)

By Steve Holland and Nandita Bose