Senate Intelligence Committee Chairman Richard Burr (R-N.C.) right, and Vice Chairman Mark Warner (D-Va.) confer on Capitol Hill, Wednesday, June 28, 2017, as the panel conducts a hearing on Russian intervention in European elections. (J. Scott Applewhite/AP)

The fate of stiffer sanctions against Russia and Iran is once again in the hands of the House, after the Senate unanimously approved technical fixes that should clear the way for the House to pass the legislation.

But even if House lawmakers move relatively quickly, it may not be fast enough to satisfy Democrats.

Senate Minority Leader Charles E. Schumer (D-N.Y.) said Thursday that he and Senate Majority Leader Mitch McConnell (R-Ky.) had hoped that Congress would approve the bill stepping up sanctions against Iran and Russia before President Trump meets with Russian President Vladimir Putin next week on the sidelines of a Group of 20 summit in Germany.

“It’s critical, critical that Congress speak in a loud and clear and unified voice to President Putin: Interfering in our election, the wellspring and pride of our democracy, will not be tolerated,” Schumer said.

The Senate passed the bill by an overwhelming 98 to 2 vote, one day after expressly approving the comprehensive Russia sanctions portion of the measure by a vote of 97 to 2. In addition to codifying existing sanctions and imposing new ones, the bill takes the rare step of giving Congress at least 30 days to review any steps the president wants to take to change sanctions policy — effectively a chance to bar the president from rolling back existing punitive measures.

The president’s warm approach to Russia, and his reticence to accept the intelligence community’s conclusion that Russia was behind a series of hacks and disinformation campaigns that colored the 2016 U.S. elections, have given many lawmakers in both parties pause. But in the last week, Democrats began to suspect that House Republicans were intentionally slowing the sanctions bill down at Trump’s behest.

The overwhelming vote in the Senate, as well as sentiments toward Russia in the House, suggested that there would be veto-proof support for the measure in Congress.

But senior administration officials said last week that the president’s team planned to step up its lobbying against the measure, objecting especially to the provision that restricts Trump’s moves absent congressional approval.

Against that backdrop, the House’s request that the Senate make technical changes to get around a constitutional problem arising from the bill’s potential to affect government revenue struck many Democrats as an excuse.

Some resisted approving the minor changes the Senate passed on Thursday until they felt they could get a guarantee from the House that the measure would be immediately put on the floor. Senate Foreign Relations Committee Chairman Bob Corker (R-Tenn.), a chief negotiator on the bill, charged Democrats with stalling, accusing them of being “Russia’s best friend” by slowing matters down.

It is not clear whether Senate Democrats ever got that guarantee, but on Thursday, Schumer announced his support for the measure with a threat directed at House Speaker Paul Ryan (R-Wis.).

“I want to put the House on notice: If they water down the bill, weaken the sanctions, add loopholes to the legislation, they will find stiff resistance here in the Senate,” Schumer said.

House leaders bristled at the accusation — but have not offered many assurances that they will, in fact, move the bill to the floor instead of putting it before the four committees of jurisdiction for formal debate. Democrats believe that such a process would end up diluting the bill.

House Majority Leader Kevin McCarthy (R-Calif.), a Trump ally, said Thursday that “I never try to go around the committees” — concluding that they would let the bill go “through regular order.”

Meanwhile, House Ways and Means Committee Chairman Kevin Brady (R-Tex.) said Thursday he would defer to the Foreign Affairs Committee for guidance “on timing and process.”

That deference may be a good thing for Democrats, as the chairman of that committee, Rep. Edward R. Royce (R-Calif.), has long called for stiffer measures against Russia for its aggression in Ukraine and support for the Syrian regime. The sanctions bill covers both, and imposes new measures to punish Russia for its alleged meddling in the 2016 election.

In an appearance on Fox News this week, Royce said: “Our goal is to pass this measure as soon as possible. We need to send this message to Putin and to Russia that there will be consequences.”