President Obama came under mounting pressure on Tuesday to take tougher steps against Moscow amid criticism that the U.S. response to Russia’s intervention in Ukraine has been too weak.

Calls for more muscular actions, from expelling Russia from the Group of Eight to offering military support to Ukraine, came as Russia’s stock market rallied and the ruble gained value a day after Obama authorized an initial round of sanctions meant to punish the Russian economy.

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House Majority Leader Eric Cantor Eric Ivan CantorThe Hill's Campaign Report: Florida hangs in the balance Eric Cantor teams up with former rival Dave Brat in supporting GOP candidate in former district Bottom line MORE (R-Va.) called on Obama to “reassess” his entire approach to Russia, while 2012 GOP presidential candidate Mitt Romney criticized Obama’s foreign policy as promoting U.S. weakness.

The White House bristled at that criticism, arguing Romney and others were misreading history.

Cantor did not directly criticize Obama’s actions, but his statement suggested serious worries that the overall response from the U.S. government has been weak.

He called for the U.S. to “dramatically” expand sanctions and formally expel Russia from the G-8. He also called for the U.S. to increase exports of natural gas in a bid to weaken the Russian economy.

“It is past time we reassess our entire strategy towards a nation that poses an increasing threat to international peace and security,” Cantor said in a statement.

While the right has heaped criticism on Obama, Congress last week failed to move legislation authorizing sanctions against Russia or providing aid to Ukraine, despite a pending vote in Crimea on seceding from Ukraine and joining Russia.The House passed a Ukraine aid bill but divisions among Senate Republicans over International Monetary Fund reforms stalled a rival aid bill in the Senate.

On Sunday, voters in Crimea decided to join Russia in a referendum the administration described as corrupt.

Critics and supporters of Obama say his hand has been weakened by U.S. fatigue with an era defined by the wars in Iraq and Afghanistan. But the president’s most vociferous opponents say Obama has exacerbated the situation with his actions, most notably on Syria.

Sen. John McCain John Sidney McCainMcSally says current Senate should vote on Trump nominee Say what you will about the presidential candidates, as long as it isn't 'They're too old' The electoral reality that the media ignores MORE (Ariz.), the Republican bested by Obama in the 2008 race, said U.S. credibility was eroded when Obama stepped back from threatened military action in Syria, despite his proclaimed “red line” against chemical weapons use.

Obama’s own advisers were surprised by his decision last September to ask Congress for authorization to strike Syria.

It quickly became clear that Congress would not do so, and Putin eventually brokered a deal in which military action was avoided and Syrian President Bashar Assad gave up his chemical weapons. More than six months later, Assad has consolidated his power, and there have been complaints about the degree to which he has given up his weapons.

“The assessment that Putin made after taking to Obama to cleaners on Syria was ‘I can do whatever I want,’ ” said Danielle Pletka of the American Enterprise Institute.

“Obama’s profile has been so weak that it has encouraged leaders who have contempt for weakness like Putin to take advantage.”

Romney charged in a Wall Street Journal op-ed that Obama’s team had been too hesitant to impose penalties against Russia, and to respond to foreign policy crises in general.

“Able leaders anticipate events, prepare for them, and act in time to shape them,” he said.

He accused the Obama administration of failing to act when action was possible and was needed.

White House press secretary Jay Carney said it was “preposterous” and “provably wrong” to link Russia’s aggression to the administration’s hesitancy in Syria.

“As others have said, the fact that President George W. Bush invaded Iraq and had two ongoing wars in the Middle East didn’t seem to affect Russia’s calculations when it came to its actions in Georgia. So there’s a problem with the logic,” he said, referencing the short 2008 war between Russia and another former Soviet bloc country.

As for the sanctions, Carney insisted penalties would deepen over time.

“I wouldn’t, if I were you, invest in Russian equities right now, unless you’re going short,” Carney said.

Pletka said Crimea, a region that was once part of Russia and that has a Russian-majority ethnic population, was now likely gone. She said the U.S. needed to take stronger actions to prevent Russia from annexing additional territory in eastern Ukraine, such as sanctioning Putin himself.

McCain has also called for the U.S. to work with NATO to come up with a long-term support program for Ukraine’s military, and to organize a civilian monitoring mission through the Organization for Security and Cooperation in Europe, among other steps.

There were some signs Tuesday that the crisis would not escalate. Putin said Russia had no plans to annex additional regions, and that was another reason for a global bull market on Tuesday.

The White House also announced members of the G-8 minus Russia would meet next week at The Hague to discuss how to respond to the Russian aggression — a signal that expulsion could be imminent. Vice President Biden was dispatched to Poland in a bid to reassure NATO allies of U.S. commitment to the region, and the U.S. is sending F-16 fighters to the country.

Bruce Jones, director of the Brookings Institution Project on International Order and Strategy and the author of a new book on American leadership on the global state, said the U.S. must work to bolster the government in Kiev.

Jones contends that the U.S. and Obama can win the long game if the administration is able to maintain the support of countries like India and China, which notably abstained during a United Nations Security Council vote condemning the Crimea referendum. He also called the crisis an opportunity to strengthen and reinforce ties with Europe.

“If we look six or seven years down the road, the likelihood is that we see stronger ties between the U.S. and Europe on energy and trade, and that strengthens the U.S. and hurts Russia,” he said.