U.S. lawmakers and senior officials hope new sanctions, cooperation with Europe and tough talk can head off Russia’s ambitions.

As voters in the Crimean region opted Sunday to break from Ukraine and join Russia, Obama administration officials offered condemnations of the election and of Russian President Vladimir Putin’s government.

“This referendum is contrary to Ukraine’s constitution, and the international community will not recognize the results of a poll administered under threats of violence and intimidation from a Russian military intervention that violates international law,” said White House press secretary Jay Carney. “No decisions should be made about the future of Ukraine without the Ukrainian government.”

Despite reports that the United States and Russia were working to seek a resolution to the Ukraine crisis, Washington remains focused on finally getting a package of Ukraine aid and Russian sanctions through Congress while coordinating with European allies to isolate Rusia economically and politically.

(Earlier on POLITICO: Corker: Kerry comments 'not helpful')

“We are putting as much pressure on the Russians that we can to do the right thing,” White House Senior Adviser Dan Pfeiffer said Sunday on NBC’s “Meet the Press.”

“We have given them the opportunity to deescalate and get this in the right place, because they know there are costs to their action here. The costs are economic. The Russian economy, the Russian stock market and ruble are at five-year lows,” he said.

Lacking military options or a way to prevent the referendum, lawmakers and the Obama administration are using the United States’s global megaphone to continue hammering Putin through rhetoric and economic threats.

Secretary of State John Kerry spoke Sunday to Russian Foreign Minister Sergey Lavrov.

“Secretary Kerry reaffirmed that the United States considers the ongoing referendum illegal under Ukrainian law and restated that the United States will not recognize the outcome,” a senior State Department official said.

Pfeiffer bluntly said that the United States won’t recognize the referendum in the Crimean Peninsula to join Russia, and he was joined by senators who denounced the vote as “bogus” and a “sham.”

“This election-referendum is a lame excuse by Putin to invade Crimea and take it over,” said Senate Majority Whip Dick Durbin (D-Ill.) on “Meet the Press. “This is a Soviet-style election, we know what the ending is going to be.”

(Earlier on POLITICO: White House: U.S. to ignore Crimea vote)

Having already moved past the controversial referendum — which the White House argues violates international law — the administration has begun executive action on sanctions targeting Russian officials, which the U.S. hopes to roll out this week with Europe. But Capitol Hill will be much more tricky.

Durbin was among a group of senators who just returned from Ukraine in a show of solidarity with Ukraine’s new government. But their actions in the Capitol betray the unity the bipartisan group showed by traveling overseas together.

Rather than serving as an example of Congress’s resolve, the debate over Ukrainian aid has instead become a heated partisan battle, with GOP leaders unwilling to sign off on the Senate’s comprehensive Ukraine bill because of its reforms to the International Monetary Fund.

Lawmakers on Capitol Hill must quickly iron out their differences over a weeklong recess if they have any hope of speaking with a unified voice — and senators sounded hopeful they can do that.

“As soon as we get to Washington, you’ll see the Senate and the House pass an economic aid package, including sanctions,” Sen. Chris Murphy (D-Conn.), the chairman of the Senate Foreign Relations Subcommittee on European Affairs, said on ABC’s “This Week.”

Even then, it might not be enough to make Russia pause in further incursions into Crimea or Ukraine, both of which were part of the Soviet Union.

“It’s going be difficult, let’s face it. Russia has always had its eye on Crimea, it considers Crimea part of Russia. So, that’s going to be difficult. But all you can do is increase the costs significantly and hope that they don’t move further into Ukraine,” Sen. Jeff Flake (R-Ariz.) said on NBC.

(POLITICO's full coverage of the crisis in Ukraine)

There are also some who want to go further.

Sen. John McCain (R-Ariz.) said on CNN’s “State of the Union” that he’s pushed Kerry to provide military assistance to Ukraine and put up a missile defense shield in Europe. He called economic sanctions a “very important step” but said the U.S. needs to think bigger still.

“There’s no contemplation of U.S. military action,” he said, “but there’s a whole lot of things the United States of America could do.”

Pfeiffer would not explicitly say that the White House is mulling any military aid at this point, preferring to focus on lobbying Congress to pass an aid bill that, combined with executive action, could cripple Russia’s economy.

But the White House doesn’t seem to be ruling anything out, either.

“Supporting the new Ukrainian government is the top of our priority list. We’re looking at all ways of assistance,” Pfeiffer said.

And though Congress and the administration agree on the broad outlines of moving forward with Russian sanctions and political and diplomatic assistance to Ukraine, Republicans are still fretting that the United States isn’t being firm enough with Putin.

Despite backing most of the administration’s actions thus far involving Ukraine, Senate Foreign Relations Committee ranking member Bob Corker (R-Tenn.) described Kerry’s rhetoric as “not helpful” and insufficiently tough. Corker’s remarks on “Fox News Sunday” underscore the tightrope Kerry must walk as he continues negotiating with Lavrov on agreeing to ratchet back Russia’s aggression.

McCain was even more critical, urging a “fundamental reassessment” of the U.S. relationship with Putin and the end of the infamous “reset” with Russia.

“God knows what Vladimir Putin will do next. He believes Ukraine is a vital part of his vision of the Russian Empire. And we need to understand that and act accordingly,” McCain said.

Jonathan Topaz contributed to this report.