New U.S. intelligence assessments say there are more indications than ever that Russia could invade eastern Ukraine, as congressional lawmakers reacted with alarm to Vladimir Putin's rapidly expanding military buildup along the border.

"The thinking in the U.S. government is that the likelihood of a major Russian incursion into Ukraine has increased," a senior U.S. official told Fox News.

The new thinking is based mostly off analysis of public information, such as heightened rhetoric from Putin and his claims that Russian-speaking people in Ukraine face "brutality." He is building a public case for more military action, according to senior U.S. officials.

Also significant is the large buildup of Russian forces along the border with Ukraine.

U.S. Defense officials say the numbers of troops far exceeds the amount needed for a training exercise. And the fact that there is no real evidence any large-scale exercises have occurred, and that none of the troops have returned to their bases, is also concerning to U.S. observers.

Some have estimated the troop strength to be at about 30,000 -- Rep. Michael Turner, R-Ohio, though, claimed Thursday that the number could be as high as 80,000. It is believed that an additional 50,000 troops may have flooded the region in the last few days.

These indications are contributing to a growing sense of alarm in Washington.

"I can't tell you how awful this is," said one congressional source who spoke to Fox News on the condition of anonymity.

In Rome as part of an overseas tour, President Obama stressed the need for the U.S. to support Ukraine. The Senate, shortly after noon, approved the first major Ukraine aid bill -- one which also includes sanctions against Russia. The House approved a different version, but each would provide $1 billion to Ukraine, and lawmakers are trying to iron out the differences before the end of the day.

The massive troop buildup along the border is reminiscent of Russia's military movements prior to the conflicts in Chechnya and Georgia, one official said.

A Defense official said if Russia were to invade the mainland, Ukraine would attempt to defend itself and this would be "far from a bloodless event as we saw in Crimea." However, Ukraine would be outmatched, this official said.

The latest assessment offers a consensus view of intelligence agencies and the U.S. military. The assessment also takes into account that Putin likely has the desire to create a land bridge into Crimea.

Putin may also believe that if he is to pay a price with the international community in the form of sanctions, he is better off getting everything out of this incursion that he wants, one senior U.S. official told Fox News.

Amid the warnings, the commander of NATO forces in Europe briefed lawmakers Thursday on the threat posed by Russian forces.

Gen. Philip Breedlove, NATO's supreme allied commander for Europe, gave a classified briefing Thursday morning to members of the House Armed Services Committee. He plans to give several briefings, including on the Senate side.

"We're all concerned about what Russia is doing on the border of Ukraine," Breedlove said after the first briefing. "The size of the forces have a message that are not congruous with respecting the borders."

After the briefing, one committee aide said: "Nothing that happened in the briefing calmed the sense of alarm expressed by members yesterday."

Republicans on the House Armed Services Committee on Wednesday strongly urged President Obama to take a firmer stance against Russia.

The letter, by eight congressmen, comes after U.S. and European security agencies estimated that Russia has deployed military and militia units totaling more than 30,000 people along its border with eastern Ukraine, Reuters reported.

The letter's authors said they are "gravely concerned" about the reported troop buildup, and urged the Obama administration to work with NATO allies to share intelligence with the Ukrainian government so they can prepare for any further incursions by Russia.

"There is deep apprehension that Moscow may invade eastern and southern Ukraine, pressing west to Transdniestria, and also seek land grabs in the Baltics," they wrote.

In a statement accompanying the letter's release, committee chairman Rep. Buck McKeon, R-Calif., said Russia's "war on Ukraine has already started."

"It is time to stop speculating about possibility, and start dealing with reality," McKeon said. "Continued inaction by the President in the face of Mr. Putin's invasion will make further Russian aggression more -- not less -- likely. Any show of resolve from the White House will have my full support."

Over the weekend, Breedlove raised the possibility that Moscow could move to expand its territory by annexing Transdniestria, a breakaway state whose 1990 claim of independence from the former Soviet republic of Moldova has gone unrecognized by the rest of the world.

"It's remarkable concern," one source said Wednesday. "There are senior people here are more concerned than I have ever seen them." A third source said that information received on Capitol Hill Wednesday "reflects a deteriorating situation which prompted very serious concern."

Fox News' Justin Fishel, James Rosen, Chad Pergram and Nick Kalman and The Associated Press contributed to this report.