Lawmakers specifically are pushing for military aid to the Ukrainian government and broad sanctions on sectors of the Russian economy that go far beyond what has been implemented to date.
Sen. Lindsey Graham, R-S.C., said Sunday the U.S. should aim to "drive the Russian economy into the ground."
The administration imposed a new round of sanctions last week targeting Russian individuals and businesses.
President Obama warned so-called "sectoral sanctions" could be next if the situation escalates, while voicing hope that a May 25 election will be a turning point.
But Sen. Kelly Ayotte, R-N.H., speaking on "Fox News Sunday," said the elections will be too late.
She said stronger measures need to be imposed "now."
"We already see the playbook of what happened in Crimea happening in eastern Ukraine. And it's time to impose tougher sectoral sanctions, provide support for the Ukrainian military," she said.
"And at this point, Russia is not getting the message."
Ayotte is among the senators backing a bill that would impose such broad-based sanctions on Russia, as well as send weapons to Ukraine.
Clashes over the last several days have brought the conflict in Ukraine, some officials say, to the brink of war.
Dozens were killed Friday in Odessa, after a building that government opponents were in caught fire when pro-government protesters threw firebombs.
Ukraine's interim prime minister accused Russia and anti-government protesters on Sunday of orchestrating a "real war."
The former U.S. ambassador to Russia, Michael McFaul, gave a similarly ominous assessment in an interview with Time.
After Ukraine's military began a major offensive to retake control of eastern cities, McFaul reportedly said Vladimir Putin may be preparing for an invasion.
"This is real," McFaul told Time.
"This is war."
Graham, speaking on CBS' "Face the Nation," agreed.
"I fear now that there will be a civil war," he said, predicting that the May 25 election cannot go forward, as "Putin has successfully dismembered Ukraine."
Graham, echoing Ayotte, called for sanctions on whole sectors of the Russian economy, including the energy and banking sectors.
The senator complained that the last round failed to dent the Russian markets, adding "it should have been called the Russian economic recovery act."
Further, he backed efforts to help arm the Ukrainian people "so they can defend themselves."
"President Obama is delusional about what's going on in Ukraine," he said.
As violence escalates, many in Congress are pushing the administration to move faster, and threatening to take action on their own.
Democratic Sen. Joe Manchin, of West Virginia, told Fox News on Sunday that he would "absolutely" support the Republican-authored sanctions bill that was announced last week.
"Everything and anything that we possibly can do should be done," he said.
Speaking on CNN's "State of the Union," Sen. Ron Johnson, R-Wis., also said:
"We really should provide some defensive weaponry, anti-tank weapons, to Ukraine."
Obama defended his foreign policy approach last week during a press conference in the Philippines, explaining that it doesn't take actions simply because "somebody sitting in an office in Washington or New York thinks it would look strong."
He said that "may not always be sexy," but it "avoids errors."
Rep. Adam Schiff, D-Calif., said on "Fox News Sunday" that stronger sanctions are needed, but the challenge now is getting European allies on board.
"I like to see stronger sanctions, but I want to see them done in concert with our allies," he said.
Source: FOX News