WASHINGTON (Reuters) - U.S. Supreme Court Justice Ruth Bader Ginsburg has a message for liberals who have been saying the 81-year-old should step down while Democratic President Barack Obama is in office so he can appoint her successor: Who are you going to get who will be better than me?

Referring to the political polarization in Washington and the unlikelihood that another liberal in her mold could be confirmed by the Senate, Ginsburg, the senior liberal on the nine-member bench, asked rhetorically, “So tell me who the president could have nominated this spring that you would rather see on the court than me?”

Ginsburg, in a wide-ranging 75 minute interview with Reuters in her chambers late on Thursday, also acknowledged that President Barack Obama had invited her to a private lunch last summer at the White House. It was an unusual move, she conceded.

Responding to questions about whether Obama might have been fishing for information about possible retirement plans, Ginsburg said, “I don’t think he was fishing.”

Asked why Obama invited her, she said, “Maybe to talk about the court. Maybe because he likes me. I like him.”

“I don’t remember the specifics, but we did talk about the court,” she added.

She said she did not believe the president’s invitation arose from any pressure to retire before this November’s congressional elections, which could change the Senate from a Democratic to a Republican majority and make the confirmation of an Obama nominee more difficult.

The court is divided between five conservatives and four liberals, and many of the hottest social dilemmas are narrowly decided. They often come down to 5-4 votes, with the liberals sometimes prevailing as they are joined by centrist conservative Justice Anthony Kennedy.

Ginsburg was appointed by Democratic President Bill Clinton in 1993.

Ginsburg’s future has been the subject of constant speculation, particularly because she has survived two serious rounds with cancer, in 1999 and 2009. She said on Thursday that she undergoes regular medical check-ups for cancer - a recent one showed no signs of trouble, she added - and works out twice a week with a personal trainer.

“Thank goodness I haven’t slowed down,” she said, asserting that she does not intend to leave the bench in the near future unless her health changes. She has previously told reporters that she wanted to remain on the court until she matches the tenure of Justice Louis Brandeis, who retired at 82 in 1939 after nearly 23 years on the court. As she nears that marker, she said she is taking it year by year.

Asked what she believed Obama might think about her future, she said, “I think he would agree with me that it’s a question for my own good judgment.”

Among those liberals who have called for Ginsburg to step down is Erwin Chemerinsky, dean of the University of California, Irvine, law school. He had asserted that only if she resigned this summer, before the November elections, could she ensure that Obama would be able to choose a successor who shares her views.

Ginsburg said on Thursday that even if she had retired, the president would have been more likely to have chosen a compromise candidate than a liberal.

Some liberals are further concerned that if she does not retire during Obama’s presidency and a Republican is elected as his successor in 2016, Ginsburg would end up being replaced by a conservative justice, moving the court even more to the right.

Ginsburg, who has been the high court’s senior justice on the left since the 2010 retirement of John Paul Stevens, has become a strong leader of that bloc and a robust voice for liberalism.

In passionate dissenting statements from the bench, she has challenged the conservative majority’s curtailing of federal voting rights law and, just in June, its position that for-profit employers can opt out of birth control coverage under federal healthcare law for religious reasons.