US Republican Donald Trump remains defiant in the face of calls for him to abandon the US presidential race, while attacking prominent Republicans and saying he has "tremendous support" despite a storm over his vulgar comments about women.

Hours out from his debate with Democratic US presidential candidate Hillary Clinton and a month away from the November 8 election, Mr Trump has taken to social media to try to squash speculation he could leave the race.

"Tremendous support (except for some Republican leadership"). Thank you," Mr Trump wrote on Twitter.

"So many self-righteous hypocrites. Watch their poll numbers - and elections - go down!" Mr Trump tweeted, apparently referring to Republican lawmakers seeking re-election who have withdrawn their support for him over a 2005 video that emerged on Friday.

Mr Trump, then a reality TV star, is heard on the video talking on an open microphone about groping women and trying to seduce a married woman. The video was taped only months after Mr Trump married his third wife, Melania.

The controversy has pitched Mr Trump, 70, into the biggest crisis of his 16-month-old campaign and deepened fissures between him and establishment Republicans.

The pressure on him will be intense at the 9pm (local time Sunday night) debate at Washington University in St. Louis. CNN reported the first questions would be about the video.

Ms Clinton communications director Jennifer Palmieri told reporters on Ms Clinton's campaign plane: "We understand that this is uncharted territory ... to face an opponent that is in the grips of a downward spiral in terms of his own party belatedly walking away from him."

A source close to the campaign of Mr Trump's vice presidential running mate, Mike Pence, dismissed talk among some political analysts the Indiana governor might bolt the ticket in the uproar over Trump's comments.

"Absolutely not," the source told Reuters.

At a Democratic campaign event in Chicago, President Barack Obama weighed in on the controversy, saying Mr Trump has been degrading not only to women, but to minorities, immigrants, people of other faiths, and the disabled.

Mr Obama said that "tells you he is insecure."

"He pumps himself up by putting other people down," Mr Obama said.