“Ric Grenell not getting confirmed is an embarrassment,” Mr. Hewitt told Senator Lindsey Graham, Republican of South Carolina, on a broadcast this month.

“Would you go to the leader and get that scheduled?” Mr. Hewitt said. “I just can’t get over this.”

Mr. Grenell, who quietly helped with Mr. Trump’s transition process, was the longest-serving American spokesman at the United Nations, working with four United States ambassadors there and especially closely with Mr. Bolton, a staunch foreign policy conservative. Mr. Grenell declined to comment for this article, but he has told allies that he would not take a job at the National Security Council under Mr. Bolton and that he is committed to the ambassadorship.

Senate officials from both parties said a senator appeared to have placed a hold on his nomination, which means moving forward with a vote would require 30 hours of debate, burning up most of a business week. Senate rules do not require the name of the legislator requesting the hold to be made public.

Last week, when the Senate majority leader, Mitch McConnell of Kentucky, called for Mr. Grenell to move ahead by unanimous consent, which requires a voice vote, Senator Jeff Merkley, Democrat of Oregon, declined to advance the nomination.

Democrats cite concerns about Mr. Grenell’s vocal criticism of the news media on Twitter as a concern.

In particular, he excoriated as biased journalists who did not report on the revelations in the hacked emails from the Hillary Clinton campaign chairman, John D. Podesta, when they were made public by the website WikiLeaks.

Senator John Barrasso, Republican of Wyoming, said the Senate needed to change the rules to speed up the process.