Leadership at NBC raced to contain an escalating revolt on Monday as some of the country’s best-known television anchors took the extraordinary step of criticizing their network on its own airwaves for hiring Ronna McDaniel, the former chairwoman of the Republican National Committee, as a political analyst.

One day after Chuck Todd stunned executives on Sunday by denouncing Ms. McDaniel’s appointment on “Meet the Press,” Joe Scarborough and Mika Brzezinski opened “Morning Joe,” one of the most influential shows on MSNBC, with criticism of Ms. McDaniel. The hosts labeled her “an anti-democracy election denier” and urged their bosses to reconsider her employment.

“We’ve been inundated with calls this weekend, as have most people connected with this network, about NBC’s decision to hire her,” Mr. Scarborough told viewers. “We weren’t asked our opinion of the hiring, but, if we were, we would have strongly objected to it for several reasons.”

Executives were bracing for another round of on-air criticism later on Monday, when two other MSNBC stars, Nicolle Wallace and Rachel Maddow, are scheduled to host their programs.

The rebellion was not limited to marquee talent. Inside NBC’s 30 Rockefeller Plaza headquarters in Manhattan, some rank-and-file employees were starting discussions on how to further pressure network leadership over Ms. McDaniel, a person with knowledge of the talks said.