A key Senate committee on Wednesday approved legislation that would bar members of Congress, the president and the vice president from trading stocks, after its Republican sponsor changed the bill to ensure that a divestment requirement included in the measure would never apply to President Trump.

The legislation, sponsored by Senator Josh Hawley of Missouri, attracted an unusual coalition of supporters, winning approval from the Senate Homeland Security and Governmental Affairs Committee with every other Republican on the panel in opposition and Democrats unanimously in support.

Senator Rand Paul, Republican of Kentucky and chairman of the committee, tried to chip away at Democratic support by framing the measure as one that would protect a president they despise. He noted that Mr. Hawley’s original proposal would have required the president and the vice president to divest starting in 2027.

“The substitute protects Donald Trump; the original bill does not protect Donald Trump,” Mr. Paul said. “I hope everyone will think about that. I would oppose the substitute change because I think it should apply to everybody or nobody.”

The measure’s fate was uncertain given the degree of Republican opposition. A White House official said substantial questions about the legislation remained.

Mr. Trump himself was noncommittal about the bill on Wednesday, telling reporters at the White House: “I like it conceptually. I don’t know about it, but I like it conceptually.”