The timing of the exchange was conspicuous: It occurred five days after a less-than-collegial moment between reporters at a presidential news conference.

Speaking in Britain last week, Mr. Trump declined to take a question from Jim Acosta of CNN, declaring his employer “fake news” and turning to John Roberts of Fox News, adding, “Let’s go to a real network.” Mr. Roberts asked his question without acknowledging the presidential slight. (Later, Mr. Roberts issued a statement saying Mr. Trump’s CNN comment was “unfair”; he did not mention Mr. Acosta.)

That moment has become a topic of heated discussion among White House reporters, who have privately debated how aggressively they should work together to get their questions answered.

Teaming up against Ms. Sanders might allow reporters to better parry her efforts to duck questions she dislikes. But a group revolt — which many Trump critics have yearned for — could also come across to viewers as pompous and self-serving. And it would likely further strain relations with a White House that is already stingy about doling out information useful to journalists and their audiences.

Still, no previous president publicly declared that the media was “the enemy of the people,” which Mr. Trump did as recently as this past weekend. And the president’s claim on Tuesday, that he had misspoken in Helsinki about Russia’s role in the 2016 presidential election, struck many reporters as implausible.

Adding to the tension, Ms. Sanders used the start of Wednesday’s briefing to chastise the press corps again, accusing reporters of engaging in a “massive media hysteria” over alleged ties between Russia and the president. She cited an erroneous tweet by a reporter for Mic News — which was deleted, but not before it raced around social media — as evidence that the press “has gotten totally out of control.”

“You guys need to take a step back,” she said.

Then came the tag-team effort from NBC News and The Hill.