Sen. John McCain, R-Ariz., on Sunday expressed concerns over Tillerson's potential selection. "It's a matter of concern to me that he has such a close personal relationship with Vladimir Putin," McCain said on CBS, adding that deals between Exxon Mobil and Russia "would color [Tillerson's] approach to Vladimir Putin and the Russian threat."
Sen. Marco Rubio, R-Fla., a member of the Foreign Relations Committee that would hold hearings for Tillerson, tweeted on Sunday that "being a 'friend of Vladimir' is not an attribute I am hoping for."
Republicans will only need a simple majority to approve Trump's nominees after Democrats removed the filibuster as an option during the 113th Congress. But only two Republicans would have to change sides to block any nominee. Fresh reports of Russian hacking of the U.S. presidential election could make Tillerson's hearings a flashpoint for bipartisan concerns over Putin's connections to the incoming administration.
Contentious hearings over Tillerson and Russia may not be what the new White House wants in its early days as it prepares to preside over Obamacare repeal and a large tax cut and infrastructure spending package.
And Tillerson is not the only nominee who could face significant opposition. Democrats will look to attack attorney general nominee Jeff Sessions' record on civil rights. And progressives are preparing a full-scale attack on Treasury secretary nominee Steve Mnuchin over his role as CEO of OneWest Bank during the economic meltdown of 2008 and 2009 and the foreclosure crisis. OneWest's aggressive foreclosure practices came in for heavy criticism during the crisis and Democrats hope that some Republicans will be swayed by stories of foreclosures in deeply red states.
One judge in 2009 described OneWest's efforts to remove a family from their home as "harsh, repugnant and repulsive." In 2011, protesters marched outside Mnuchin's home in Los Angeles with signs reading "Stop taking our homes."
The progressive playbook on Mnuchin is also counting on the extensive financial disclosure required of Cabinet nominees to be embarrassing for the Treasury nominee. The left will also use Mnuchin's hearings as opportunity to showcase what they view as the overwhelming influence of the financial industry in the administration of a candidate who campaigned on a populist, anti-Wall Street message. Trump regularly criticized opponents for their ties to banks, especially Goldman Sachs. Mnuchin spent 17 years at Goldman. Trump is also eyeing Goldman President Gary Cohn to serve as director of the National Economic Council. Steve Bannon, incoming senior White House adviser, also began his career at Goldman.
Democrats' main goal over the next two years is to recapture their status as the party of the working class and not just of coastal elites. And teeing off on Mnuchin will be a key part of kicking off that strategy in 2017.
Still, it's unlikely that Republicans will defect and block Mnuchin's nomination unless major revelations come to light. The same cannot be said of Tillerson.
If Democrats can show that the Exxon Mobil CEO's financial ties to Putin and Russia would cloud his judgment as America's top diplomat, the nomination could wind up in serious trouble.
This could be one reason why the Trump team has floated Tillerson as the likely nominee without actually announcing anything. They likely want to see just how great Republican opposition will be. If it appears over the next couple of days that Tillerson's hearings would be an unwelcome distraction, Trump could shift gears yet again and go with one of the many other names floated for secretary of State.
If he sticks with Tillerson, 2017 could get off to a tough start for the new occupant of the Oval Office.
—Ben White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.