Still, there are some signs that Mr. Colbert’s show is picking up steam, especially with the Trump administration in its earliest days. On Friday, the day of the inauguration, Mr. Colbert had his best ratings in over a year.

The Emmys, which will be broadcast on Sept. 17, have had ratings problems; each of the last year two years it has had record lows in viewership.

In a nod to comments by the White House press secretary, Sean Spicer, on Saturday about the size of the crowd at President Trump’s inauguration, Mr. Colbert said in a statement: “This will be the largest audience to witness an Emmys, period. Both in person and around the globe.”