The proposal asked that the shows be allowed to use their writers and committed them to the same terms Mr. Letterman’s company had agreed to. The request was never formally turned down, though an executive associated with the shows said, “We were told it wasn’t looking good.”

On Monday, guild members picketed both shows, with about 15 people outside Mr. Stewart’s studio .

Courtney Simon, a striker who formerly worked as a script editor on “As the World Turns,” acknowledged some awkward feelings about protesting against Mr. Stewart, whose show she said she loved.

“He is a member of the guild,” she said. “But we are on strike against the studios. There are certain things that have to be done, and this is one of them.”

Most of the picket signs at both locations had messages aimed at Viacom, the parent company of Comedy Central.

The denial of the request for an interim agreement left representatives of the two programs and Comedy Central disappointed and, the executive associated with the shows said, “confounded by the fact that the decision was so arbitrary.”

What most upset those involved in the effort was that the union gave no special consideration to the Comedy Central shows, even though the guild regarded it as a coup when it won a contract for “The Daily Show” in 2006. The series had just won an Emmy for best writing.

Like the other hosts whose shows have been picketed by the guild, including Jay Leno and Conan O’Brien on NBC and Jimmy Kimmel on ABC, Mr. Stewart and Mr. Colbert had been paying the salaries of nonwriting staff members out of their own pockets.