WASHINGTON — Before President Trump was even sworn into office, congressional Republicans made a pledge: They would be a check on executive power, they said, often making the independence of the legislative branch a centerpiece of their own election campaigns last year.

But on Wednesday, Senator Mitch McConnell, Republican of Kentucky and the majority leader, sought to give the beleaguered administration significant cover, strongly defending the firing of the F.B.I. director, James B. Comey, and resisting calls to challenge Mr. Trump and support a broader inquiry of Russian interference in the election.

“Today we’ll no doubt hear calls for a new investigation,” Mr. McConnell said on the Senate floor as most Senate Democrats looked on, “which can only serve to impede the current work being done.”

Democrats exerted as much pressure as they could on their Republican colleagues on Wednesday, moving to shut down Senate committees, using procedural moves available to the minority to block or delay hearings on Russia, cybersecurity, presidential nominees and several other matters.