In the meeting, Ms. Hair described herself as a strong Trump supporter, according to those familiar with the events. Ms. Hair did not respond to an email seeking comment.

A central focus for Ms. Hair and Ms. Thomas was administration appointments that they wanted made and that they accused the president’s aides of blocking. People familiar with the situation indicated that the people Ms. Hair and Ms. Thomas wanted hired were rejected for a range of reasons, and in at least one case someone was offered a job and declined it because the position was not considered senior enough. Another complaint was that Ms. Thomas had not actually shared the full list of people to be hired, said those familiar with the meeting.

Others attending included Frank Gaffney, the founder of the Center for Security Policy who has advocated curtailing immigration and has repeatedly denounced Muslims, and Rosemary Jenks, who works for the anti-immigration group NumbersUSA, according to the people familiar with the events.

Ms. Thomas — whose group, Groundswell, was formed in 2013 to strategize against Democrats and the political left and meets weekly — joined others in prayer at the start of the meeting. Some members of the group prayed at different moments as the meeting continued. At one point, Mr. Trump pulled in his daughter Ivanka, a West Wing adviser, saying she would be beloved if she were serving a liberal president, instead of getting negative news coverage.

One attendee criticized Republican congressional leaders, saying they should be “tarred and feathered,” a person briefed on the meeting said. Mr. Trump defended the Senate majority leader, Mitch McConnell of Kentucky, and the House minority leader, Kevin McCarthy of California, saying that they had held strong for nearly five weeks of a shutdown, and that it was not clear what else the attendees thought they could be doing.

Ms. Thomas, who was said to have opened the meeting by informing the assembled White House staff members that she feared being open because she did not trust the people there, has long been more conservative than her husband, and has often provoked controversy.

In 2011 she formed a government affairs firm called Liberty Consulting, which drew criticism for boasting on its website that Ms. Thomas would use her “experience and connections” to help clients.