She and Senator Patrick J. Leahy, Democrat of Vermont, said they would try to use a pending spending package to prevent Mr. Sessions from following through on the plan to overturn an Obama-era policy that made marijuana prohibition a low priority for law enforcement. Mr. Leahy noted that such a provision had previously passed the Senate Appropriations Committee with support from both parties.

The pushback was not the only bipartisan resistance coming in the middle of the furor surrounding Mr. Trump’s emphatic break with his former chief strategist, Stephen K. Bannon, in the aftermath of his reported comments in a new book about the presidency. An Interior Department plan to open much of the nation’s coastline to new oil exploration also drew strong opposition from some Republicans, including Gov. Rick Scott of Florida, a likely candidate for the Senate this year.

The new marijuana policy and the oil drilling effort could present political peril for Republicans in Colorado and states along both coasts in some of the same locales where resentment to the new tax plan has already surfaced. Politicians in both parties from Florida up the Eastern Seaboard have fought expanded oil exploration for decades, responding to strong public opinion in those states.

Senator Bill Nelson, Democrat of Florida and a longtime opponent of offshore drilling who could be facing off against Mr. Scott in a high-profile Senate contest, immediately jumped on the issue.

“This plan is an assault on Florida’s economy, our national security, the will of the public and the environment,” Mr. Nelson said. “This proposal defies all common sense, and I will do everything I can to defeat it.”

At the White House, the press secretary, Sarah Huckabee Sanders, said the administration did not intend to start a fight with Mr. Scott but would not shy away from one either.