Amid a dustup between the Trump Transition and the U.S. Intelligence Community over Russia, some Republican Senators signaled their concern Saturday over the expected choice of the Exxon Mobil CEO Rex Tillerson as Secretary of State, worried by his ties to the Russian government, as Democrats demanded public hearings in Congress about Russia's involvement in possible election interference.

"I don’t know what Mr. Tillerson’s relationship with Vladimir Putin was, but I’ll tell you it is a matter of concern to me," Sen. John McCain (R-AZ) said in an interview with Fox News.

"Vladimir Putin is a thug and a bully and a murderer," McCain said to NBC News before the Army-Navy football game. "The relationship between Mr. Tillerson and Vladimir Putin needs to be examined."

Tillerson and Exxon Mobil have had extensive dealings with the Russians, but some of their oil exploration deals have been slowed by economic sanctions placed on Russia over its actions in Ukraine and Crimea.

In an excerpt of an interview with Fox News Sunday, President-Elect Trump defended Tillerson, praising his "massive deals with Russia" as Exxon Mobil CEO.

Tillerson is no stranger to lawmakers on Capitol Hill as head of Exxon Mobil; but lawmakers are also no strangers to questions about U.S. policy with Russia, which has bubbled up in recent months over the elections.

As one might expect, Democrats demanded hearings and a fuller public explanation from the Intelligence Community about Russia's actions.

"An investigation must begin as soon as possible on any evidence Russia actively worked to hijack our election," said Sen. Patty Murray (D-WA).

"I again call on the GOP Congress to hold hearings immediately," said Rep. Brendan Boyle (D-PA).

While Democrats pressed for answers, a number of Republicans downplayed the Russian election story, raising eyebrows about suggestions that the Russians helped President-Elect Trump.

"Be skeptical of any claims from anonymous officials," said Rep. Justin Amash (R-MI).

On Friday, the Trump Transition team blistered the CIA over reports that U.S. intelligence officials believe Russia was trying to help Mr. Trump win in November.

"These are the same people that said Saddam Hussein had weapons of mass destruction," the Trump Transition said in a written statement issued Friday.

A senior intelligence official told me on Saturday there would be no public reaction to Trump's statement, as former officials mulled over the situation.

For the President-Elect's team, there was nothing here to see.

"It's time to move on," the Transition said.