The Senate on Wednesday rejected an effort to undo President Trump’s sweeping tariffs on most U.S. trading partners, even as a small group of Republicans joined Democrats in delivering a rebuke to a trade policy that many lawmakers fear is causing economic harm.

The vote deadlocked at 49 to 49, meaning it failed despite three Republicans joining Democrats in favor of a measure that sought to terminate the national emergency declaration Mr. Trump used this month to impose 10 percent reciprocal tariffs.

Senator Rand Paul, Republican of Kentucky and a cosponsor of the resolution, crossed party lines to support it, as well as Senators Susan Collins of Maine and Lisa Murkowski of Alaska. But the defections were not enough to make up for the absences of two supporters: Senators Sheldon Whitehouse, Democrat of Rhode Island, and Mitch McConnell, Republican of Kentucky, who backed a similar measure this month.

“It’s still a debate worth having,” Mr. Paul said of the failed resolution. He noted that many of his Republican colleagues are privately expressing consternation over Mr. Trump’s trade war but have carefully calibrated their public responses to defer to the president.