Washington (CNN) After weathering a week of self-induced crisis , the White House was at an impasse on Wednesday. It had been seven days since Rob Porter, the staff secretary accused of spousal abuse, had resigned . Pressure was mounting on the White House for an explanation of who knew what, and when.

Sarah Sanders, the press secretary, was frustrated, according to a source familiar with her thinking. Her latest explanation for why Porter was allowed to continue on in his high-profile job, despite officials being aware of the allegations against him, involved an obscure office squirreled away in a building on 17th Street. Staffers balked at taking responsibility for the bungling of one of the biggest crises to hit the Trump administration.

Sanders, the source said, had appealed to chief of staff John Kelly and White House counsel Don McGahn -- both of whom were generally aware of the allegations against Porter before he stepped down, making them central players in the scandal -- to brief reporters in order to provide clarity to the situation.

Some officials were also encouraging Kelly to sit down for a television interview -- likely on Fox News -- to lay out the facts of the case. Others within the White House wanted him to go further and apologize for how the matter has been handled, people familiar with the internal discussions said.

Kelly was unwilling to go that far, people familiar with his thinking said. He had been telling associates he wanted the crisis surrounding Porter's departure to end -- but had yet to express a willingness to publicly accept any blame for keeping him on staff even as his background was being flagged by the FBI.

In the end, Kelly agreed to go in front of reporters Wednesday, but the press briefing was delayed by several hours, and then canceled after a gunman opened fire on a high school in Florida. The White House didn't schedule a briefing for Thursday.

Politico first reported Sanders' frustration and Kelly's willingness to take questions. The White House did not immediately respond to a CNN request for comment.

Missed opportunity

It was a missed opportunity for a White House that has continued to reel a week after Porter's departure. Morale has plunged. Leaks are rampant. Staffers who started a year ago say the mood resembles the chaotic first weeks of the administration, when warring factions divided the West Wing and hampered Trump's agenda.

Most of the attention has centered on Kelly, who in his six and a half months on the job has largely avoided the persistent speculation about his standing that has dogged some other aides. A person who has spoken with Kelly says he's mostly concerned about the plummeting morale among his staff and not the external optics of a West Wing in crisis. Kelly -- who like his boss has a stormy temper -- has fumed about the rash of leaks portraying him as a liar and doesn't understand why his underlings have shown so little loyalty amid the crisis.

Others in the White House say Kelly hasn't been suitably contrite after clear errors in judgment surrounding the Porter episode. There are few inside the West Wing who know the precise timeline about who knew what details about Porter's background and when. But there is a sense among officials that little has been done to clarify what mistakes were made and what is being done to prevent them from happening again.

During her last televised briefing, Sanders revealed new caution after her previous statements didn't match the timeline offered during testimony from the FBI director: "Not that I'm aware of." "I can't say with 100% certainty." "Again not that I'm aware of."

Speaking privately, many officials say Kelly should be the one to accept the blame in public -- even if there were others inside the White House, such as McGahn or deputy chief of staff Joe Hagin, who are at least as responsible for allowing Porter to remain in his job even after the FBI flagged concerns about his background.

Trump looks to improve the situation

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Trump, too, is at a loss for how to end the bad headlines, he told friends throughout this week. Some have advised him the only way to improve the situation is to fire someone -- anyone -- as a show of authority. But he's met those suggestions skeptically, saying it could plunge his operation into further chaos.

Though the White House insisted this week that Trump had confidence in Kelly, a source familiar with his mindset says the President is still very much frustrated with his chief of staff, and that the bungling of the Porter scandal only escalated an irritation that already existed. But there is no clear replacement for Kelly in Trump's mind, at least not yet.

Several names have been floated, but the President has expressed misgivings with each of them because they all come with their own set of complications. Gary Cohn, his top economic adviser, is a Democrat whose views are loathed by some of the most conservative members of Trump's orbit, and was himself close to being fired by the president months ago. Rep. Kevin McCarthy, the House majority leader, would come to the job having acted as a principal for years instead of an aide.

Another name that's emerged in the past days: businessman and former lobbyist Wayne Berman, whose case has been pressed by Fox News host Sean Hannity, a regular but informal adviser to Trump, a person familiar with the conversations said. It's not clear how familiar Trump is with the GOP operator.

And budget chief Mick Mulvaney is still in Trump's good graces, though people who he's spoken with say he's happy in his current job at the Office of Management and Budget.

Adding to Kelly's woes are comments his predecessor Reince Priebus has made as he promotes a new chapter in a book about chiefs of staff. Priebus, who was pushed out in favor of Kelly in July, has gleefully described a tumultuous and back-biting West Wing even worse than is depicted in the media. Inside the White House, his comments have been regarded as predictable but disloyal, and some have wondered why he appears to be kicking an already wounded West Wing.

On Wednesday, as news bulletins about the school shooting in Florida emerged, the White House turned its focus almost entirely to the massacre. The daily press briefing was canceled and Trump phoned state and local leaders to express his condolences. Aides began initial preparations for a visit to the Parkland area over the weekend, and they canceled a visit to an Orlando concrete plant on Friday that was meant to advance the infrastructure plan he revealed at the start of the week.

Trump is due to spend the President's Day weekend at his Mar-a-Lago estate in Florida, where he's been known to poll the coterie of longtime friends about staffing changes. He often travels without high-ranking staff unless he has meetings with foreign leaders planned.

This weekend, however, Kelly plans to travel with him too, a person familiar with the plans said.