Late Friday afternoon, the story broke that Donald Trump, in a 2005 conversation with a former host of “Access Hollywood,” had boasted about groping women’s intimate body parts. Photograph by The Washington Post via Getty

What should a national political party do if it discovers, four weeks before an election, that its candidate for President is a man who once described his behavior in terms that fit a sexual predator? That was the unprecedented dilemma that the Republican Party was dealing with on a remarkable Friday night, and as Saturday arrived the outcome of its deliberations wasn't entirely clear.

The bomb went off in the late afternoon, when the Washington Post's David A. Fahrenthold reported that Trump, in a 2005 conversation with a former host of “Access Hollywood,” a tabloid television show, had boasted about hitting on women, kissing them, and groping their intimate body parts. "You know, I’m automatically attracted to beautiful—I just start kissing them," Trump said in the conversation, which took place on the set of a soap opera in which Trump was making a guest appearance, and which was apparently picked up by a hot microphone. "It’s like a magnet. Just kiss. I don’t even wait. And when you’re a star they let you do it. You can do anything.” The interviewer,** **Billy Bush, then said, "Whatever you want.” To which Trump replied, “Grab them by the pussy. You can do anything.”

At another point on the tape, Trump boasted that he "did try to have sex" with a married woman, but his efforts were unsuccessful. "I moved on her like a bitch, but I couldn’t get there," he said. "And she was married. Then all of a sudden I see her, she’s now got the big phony tits and everything. She’s totally changed her look.” Elsewhere on the tape, when Trump and Bush were appraising the woman they were about to meet, Trump said, “Oh, it looks good.”

It took a few hours for the full meaning and offensiveness of Trump's remarks to filter through to the G.O.P. establishment. The first Republicans to react were some of Trump's foes, including Senator Mark Kirk, of Illinois, who said in a tweet that the candidate should “drop out. @GOP should engage rules for emergency replacement.” Kirk added, “DJT is a malignant clown—unprepared and unfit to be president of the United States.”

Other Republican critics of Trump also took to Twitter to flay him. "As the grandfather of two precious girls, I find that no apology can excuse away Donald Trump's reprehensible comments degrading women," Jeb Bush wrote. Mitt Romney was even more scathing: "Hitting on married women? Condoning assault? Such vile degradations demean our wives and daughters and corrupt America's face to the world."

One of the first senior supporters of Trump to comment was Reince Priebus, the chairman of the Republican National Committee. In a short statement issued at about eight-thirty, Priebus said, "No woman should ever be described in these terms or talked about in this manner. Ever.” Shortly after that, the office of Paul Ryan, the Republican speaker, let it be known that he had disinvited Trump from a campaign event in Wisconsin on Saturday. In a statement, Ryan said, “I am sickened by what I heard today. Women are to be championed and revered, not objectified. I hope Mr. Trump treats this situation with the seriousness it deserves and works to demonstrate to the country that he has greater respect for women than this clip suggests."

Neither Priebus, who has been working closely with the Trump campaign, nor Ryan, who reluctantly endorsed Trump after initially displaying some hesitation, mentioned anything about the candidate dropping out of the race. And they also stopped well short of saying that his remarks were so offensive they were disqualifying for a Presidential aspirant.

But the possibility of a Trump withdrawal does appear to have been broached in senior Republican circles. Shortly after Ryan released his statement, Yamiche Alcindor, a reporter for the New York Times, said on Twitter that a source had told her, “RNC officials are meeting in DC to discuss what options the party has going forward in case Trump isn't nominee." In another tweet, Alcindor reported, "Source also says that RNC officials likely can't oust Trump from the ticket and that Trump would likely have to quit on his own."

On social media, there was some talk of Trump standing down in favor of his running mate Mike Pence, an option that many establishment Republicans would embrace, at least in theory. But as the Washington Post's Philip Bump and David Weigel stressed, there would be serious obstacles to carrying out such a switcheroo. In some states, including Florida, Michigan, North Carolina, Ohio, Texas, and Virginia, the deadline for getting names on the ballot has already passed.

If Trump were to drop out and his name to remain on the ballot, the Republican Party could still urge people to vote for him in the understanding that they were really voting for Pence, but after the election they might well have to go to court to get the votes transferred to Pence. Or, at least, that is what Ballotpedia's Charles Aull, an expert on Presidential elections, told Business Insider in August, when there was also some speculation that Trump might drop out.

Trump himself gave no indication that he was considering such a thing. Shortly after the Washington Post story was published online, he issued a statement dismissing his remarks as "locker room banter, a private conversation that took place many years ago." He added, "Bill Clinton has said far worse to me on the golf course—not even close. I apologize if anyone was offended." Later in the evening, the Trump campaign issued another statement, saying that Pence would take his place in Wisconsin on Saturday. Trump said he would be remaining in New York for "debate prep with RNC Chairman Reince Priebus, Gov. Chris Christie and Sen. Jeff Sessions, and then flying to St. Louis on Sunday for the 2nd Presidential Debate." The mentions of Priebus, Christie, and Sessions by name appeared to be intended to give the impression that Trump's allies were sticking with him.

Somebody in his campaign must have thought that these statements weren’t enough, and shortly after midnight Trump released a short video, which included a more explicit mea culpa. He said, "Anyone who knows me knows these words don't reflect who I am. I said it, I was wrong, and I apologize." Trump then went on the offensive. "I've said some foolish things, but there is a big difference between the words and actions of other people," he said. "Bill Clinton has actually abused women, and Hillary has bullied, attacked, shamed, and intimidated his victims. We will discuss this more in the coming days. See you at the debate on Sunday."

Even as Republicans were digesting the “Access Hollywood” tape, other stories were emerging, or reëmerging, about Trump's sexual history, which has been a subject of gossip in media circles for months.

The Daily Beast reported on Friday night that the unnamed married woman in the “Access Hollywood” tape whom Trump tried and failed to have sex with was one of the show's former hosts, Nancy O'Dell, who also co-hosted Trump's Miss Universe contest. The Daily Beast report cited stories from 2007 that alleged Trump tried to fire O'Dell from his beauty pageant because he "didn’t like the way she looked while she was several months pregnant." On social media, meanwhile, many people pointed to an upcoming hearing in a federal lawsuit in which an anonymous woman has accused Trump of raping her in 1994, when she was only thirteen years old. A lawyer for Trump has described the charges, which were originally filed in California, as "categorically untrue and an obvious publicity stunt aimed at smearing my client.”

Regardless of the merit of that lawsuit, the “Access Hollywood” tape has refocussed attention on Trump's history of making offensive remarks about women, and openly regarding them as sex objects. Earlier this week, for example, the Associated Press reported that, during his time on the reality-television series "The Apprentice," Trump "repeatedly demeaned women with sexist language, according to show insiders who said he rated female contestants by the size of their breasts and talked about which ones he'd like to have sex with."

That is the person the Republican Party picked as its candidate for the White House. With voting day fast approaching, it is now paying the price.