“You have to be strategic, but there are issues when the Republicans are closer to us than to him,” Mr. Schumer said in a recent interview.
The sanctions plan, which has hit a snag in the House, was similar to the approach lawmakers took earlier this year on a major spending bill. They negotiated mainly among themselves and then advanced a bill that the White House didn’t particularly like but found difficult to oppose.
In that case, Mr. Schumer assiduously avoided dealing directly with the White House and worked with congressional Republicans. Lawmakers eventually agreed on a governmentwide spending measure that did not fund top Trump priorities such as a new border wall. But the administration had little choice but to accept the outcome or be responsible for shutting down the government on the occasion of its first 100 days in office.
In the current case, the proposed sanctions on Russia for interfering in the 2016 election were added to a measure putting more restraints on Iran in retaliation for nonnuclear activities such as ballistic missile testing, arms shipments and other support for terrorism. Mr. Schumer said that he approached Senator of Kentucky, the majority leader, on the Senate floor and suggested the idea of merging the two sets of sanctions. Mr. McConnell, he said, responded a day later that he would back the move.
“I thought he probably agreed with us on Russia sanctions,” Mr. Schumer said.
Mr. McConnell has been an aggressive critic of Russia. Aides said that Republicans were already planning to link the two but did not dispute that Mr. Schumer raised the idea in the floor conversation.
In the Senate, merging the Iran and Russia sanctions was seen as a win-win, giving foes of Iran a new chance to register their objection to that nation’s conduct while providing the Senate — where there is deep anger over Russia’s interference in the election — its first real opportunity to hit back for last year’s activities.
“That cannot go unchallenged,” said Senator Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee, who took up elements of the sanctions legislation initially pushed by Mr. Schumer. “We have to protect ourselves and take action when we have been attacked.”
Conservative Republicans expressed a similar view. “Many of us on both sides of the aisle feel the United States needs to be much stronger in its response to Russia,” said Senator Michael D. Crapo, Republican of Idaho.
But the entanglement of the Russia and Iran sanctions presents significant complications for the White House. The Trump administration strongly backs taking tough steps against Iran but has stated that it believes current sanctions against Russia are sufficient. And the move to grant Congress the ability to overrule the White House on sanctions is raising alarm with the administration as an infringement on executive power and a limitation on flexibility in foreign policy.
But if the White House were to now balk at the Senate legislation, the administration would lose its ability to inflict punishment on Iran and risk looking too sympathetic to Russia when its posture toward that nation is already under scrutiny by Congress, and the special counsel Robert S. Mueller III.
Senators of both parties now back congressional review of any attempt to weaken sanctions out of fear the White House might not follow through.
The White House is looking to the House to help it out of the predicament by softening the bill. And House Republicans have already shown some discomfort with the measure, raising an arcane procedural objection that was seen by senators in both parties as a gambit to buy time while House leaders figure out an approach that would satisfy lawmakers who want to impose sanctions but not alienate the White House.
House officials say they are eager to move forward once they get the procedural snag worked out.
“We want to get this bill cleaned up,” said Speaker , who said the relevant committee chairmen in the House were eager to take up the measure.
Whatever happens, the sanctions legislation showed that there are opportunities for the two parties to work together on shared policy concerns outside the partisan hot zone surrounding some of the big-ticket issues.
“There are going to be many things,” Mr. Schumer said. “They are not at the high level like taxes and health care, but they are at the next level and there is a bunch of them.”
Still, given the overall partisan intensity, the cooperation around the Iran-Russia sanctions bill and the earlier spending package will remain the exception rather than the norm. But those examples do underscore that there are moments when congressional Republicans and Democrats can come together and leave Mr. Trump the odd man out.