President Obama's handling of Russia's annexation of Crimea dominated the Sunday news shows, with members of both the Democratic and Republican Senate leadership calling on the administration to provide military aid to Ukraine as a means of potentially preventing further Russian aggression.

In separate interviews on CBS's "Face the Nation," Sens. Richard J. Durbin (D-Illinois) and Kelly Ayotte (R-N.H.) both said that the United States should provide Ukraine with whatever military equipment it needs to help ensure the Russians do not occupy or attempt to take over any other parts of Ukraine.

"This army in Ukraine was devastated by Yanukovych," Durbin said, referring to deposed Ukrainian president Viktor Yanukovych. " It is so weak now that there are maybe 6,000 troops ready to go to battle. We've got to strengthen them and help them with advice and backing, and it may come to small arms.  I'm not ruling that out; keep it on the table.  For the time being, let's help the Ukrainian army get on its feet as a self-defense force."

Those comments were later echoed by Rep. Mike Rogers (R-Mich), chairman of the House Intelligence Committee, in an interview on NBC's "Meet the Press."

"We have to take a tough stand with our European partners, there are things we can do that we're not doing." Rogers said. "We can do non-combatant military aide that allows them to defend themselves, what we can do is offer them things that they can use to really prevent and defend themselves."

Ayotte said the United States should also look into the possibility of imposing further economic sanctions.

"I think we need to do more with sanctions, including sanctioning the entire financial sector of the Russian economy, as well as looking at the energy sector," Ayotte said, later adding: "The Russian economy is a one-trick pony.  They're totally focused on natural gas and oil.  And so if we were to impose greater sanctions on economic sectors, I think we could have a significant impact on Putin and then he would get the message."

The remarks come as Congress continues to debate whether to send monetary aid to Ukraine, and as the U.S. and Russian governments carry on with what seems to be a diplomatic standoff  over the Russians' decision to annex the Crimea region -- with both governments handing down sanctions and travel bans to some of the other's lawmakers this week.

In an interview with ABC's  George Stephanopoulos, Ukrainian Foreign Minister Andrii Deshchytsia said he and other officials in Ukraine are concerned about further Russian aggression -- especially given the fact that Russian troops have taken position on the country's  border.

"We are very much concerned about this development, the deployment of Russian troops on our Eastern borders," Deshchytsia said in an interview broadcast on ABC's "This Week." "We are ready to respond and as you know the Ukraine government is trying to use all the peaceful diplomatic means and diplomatic means to stop Russians but the people are also ready to defend their homeland.”

Deshchytsia went on to say that he believes the chances of an all-out war between Russia and Ukraine are "growing."

"The problem is that Russians, and particularly the – Putin’s administration, Putin himself is not talking to the rest of the world, he doesn’t want to listen to the world," he said. "We don’t know what Putin has in his mind and what will be his decision. That’s why this situation is becoming even more explosive than it used to be a week ago."

Meanwhile, 2012 GOP presidential nominee Mitt Romney sharply criticized President Obama's handling of the Crimean situation, declaring that Obama's 'naivete' has hurt the United States' standing internationally.

"There is no question that the president's naivete with regards to Russia and his faulty judgement about Russia's intentions and objectives has led to a number of foreign policy challenges," Romney said during an interview on CBS's "Face the Nation." "Having not anticipated Russia's intentions, the president wasn't able to shape the kinds of events that may have been able to prevent the kinds of circumstances that you're seeing in the Ukraine."