Future sanctions over President Vladimir Putin’s invasion of Ukraine must focus on depriving Putin of what he needs to fund and fight the war: revenue from Russia’s oil and gas sales and access to global supply networks to replenish his military, two architects of the Biden administration’s sanctions campaign told lawmakers on Wednesday.

While calling for stronger action against Russia, the State and Treasury department officials appearing before the Senate Foreign Relations Committee faced complaints from both Democrats and Republicans that the first rounds of sanctions did not hit Moscow as hard or fast as the administration had forecast.

“What we were told was these were going to be the toughest sanctions ever on a country. That they were going to have certain impacts,” said Sen. Jeanne Shaheen, a New Hampshire Democrat, recounting early predictions from administration officials that the sanctions would plunge the country into recession, send the value of the ruble plunging, and trigger unrest among Russians. "And we have not seen the full impact that was described to us.

“The frustration is we know that while we're playing the long game, Ukrainians are dying,” Shaheen added.

Putin has vowed to press his offensive in Ukraine despite battlefield losses to motivated and NATO-supplied Ukrainian forces. Within the past week, Russia has started calling up hundreds of thousands of civilian men to replenish its depleted forces in Ukraine and held sham referendums in Russian-occupied territory, as an expected prelude to claiming those lands for Russia.

In response to those referendums, the U.S. and its allies are preparing new sanctions that White House press secretary Karine Jean-Pierre said Wednesday would impose a “severe economic cost on Russia when they move forward with annexation.”

Senators and the two Biden administration officials — Elizabeth Rosenberg, an assistant Treasury secretary, and James O'Brien, head of the State Department's sanction coordination office — focused Wednesday on additional penalties aimed at making it impossible for Russia to keep prosecuting the war.

Adroit financial management by Russian officials and, above all, billions of dollars of windfall profits from oil and gas exports have buffered the impact of the sanctions imposed by the United States and about 30 other nations. Sanctions so far have targeted Russia's financial institutions, businesses, military and high-tech industries, and thousands of officials and other members of the Russian elite.

Rosenberg told lawmakers that Russia should be in fiscal deficit by the end of the year. But Russia's currency is managing far better than the U.S. projected, and its inflation and stock market troubles aren't out of line with other countries', in a rough year overall for the world's economy, Sen. Mitt Romney, a Utah Republican, pointed out.

“It wasn't as crippling as we thought on Russia,” Romney said of the international sanctions, which, with arms supplies for Ukraine, form the core of the West's support for Ukraine. That might serve as a cautionary lesson when the U.S. considers sanctions in the future, Romney argued.

Rosenberg stressed that the U.S. should be “laser-focused” on starving Russia of the energy profits that are keeping the war and its economy going. Russia is a leading global exporter of oil and natural gas.

U.S. and European officials are rushing to complete plans for a system of price caps on Russian maritime oil exports. The system would be designed to keep Russian oil on the world market, to avoid driving up prices even higher, while forcing down the price that Russia gets for its exports.

Next in importance, the sanctions officials said, was doubling down on the global arms procurement networks Russia is using to replenish its weapons and technology for the war in Ukraine. Already, Russia is fielding older and older equipment on the battlefield, turning to Iran for drones, and, reportedly, cannibalizing commercial high-tech to keep military hardware running, O'Brien said.

Lawmakers and the sanctions officials also talked of better coordinating existing U.S. and European Union sanctions to close loopholes, of unspecified future measures against Russia's “soft power,” and of sanctions on human rights abusers in the Russian military.

“We appreciate what you do,” Sen. James Risch, an Idaho Republican and ranking member of the committee, told the sanctions organizers. “We want you to double your efforts in this regard. Because you're the ones that can really help bring this thing to an end.”