Sen. Marco Rubio of Florida, a former Republican presidential candidate who fiercely battled President-elect Donald Trump for the GOP nomination, will sit on the dais across from Tillerson. He will grill him about his company's vast business interests in Russia, his opposition to US economic sanctions against Russia and his apparently friendly relations with Russian President Vladimir Putin, who many lawmakers believe is a deceitful and dangerous dictator.
"The next secretary of state must be someone who views the world with moral clarity, is free of potential conflicts, has a clear sense of America's interests," Rubio said in a statement Tuesday, hours after Tillerson was nominated. "I will do my part to ensure he receives a full and fair but also thorough hearing."
Rubio, whom Trump repeatedly mocked and embarrassingly defeated in the Florida primary, now finds himself with significant leverage over his former rival. That's because the Foreign Relations Committee is expected to be made up of 10 Republicans and nine Democrats, meaning if he votes against Tillerson -- and all Democrats on the committee do as well -- the nomination could stall.
Usually when that happens, the president sends up a new nominee. But Senate GOP leaders, aware of the close margins for Tillerson and the President-elect's strong desire to get the non-politician confirmed, could use a backup plan.
If Tillerson were defeated in committee, according to aides in both parties, committee chairman Bob Corker, R-Tennessee, could use procedural tools and precedents to get his nomination to the floor for a confirmation vote anyway.
Corker, who has become close to Trump and was himself a finalist for the top State Department job, could ask his members to move the nomination to the floor with a vote of "disapproval" from the committee. While that label could be somewhat damaging to Tillerson, it might be worth the price if Senate GOP leaders believe they have the votes to confirm him on the floor.
Republican aides were confident Tuesday the handful of GOP critics of Tillerson would eventually support him, especially after his confirmation hearings when Tillerson will articulate his views and experience. They also noted that no GOP senator publicly came out against the nominee.
Republicans will hold a 52-48 seat advantage in the Senate next year. That means if all the Democrats vote against Tillerson, Republicans can lose two of their members and still have Tillerson confirmed if then-Vice President Mike Pence breaks the tie.
In addition, aides in each party didn't rule out that some Democrats might vote for Tillerson, especially those moderate Democrats from red states up for re-election in 2018 and those from energy-producing states who might be naturally inclined to support the influential ExxonMobil boss.
One Democratic senator who fits both of those descriptions, Joe Manchin of West Virginia, suggested he was open to voting for Tillerson.
"As West Virginia's former governor, I was able to select members of my Cabinet and key advisers, and I have always believed that a President should be able do the same. With that in mind, I look forward to using the confirmation process to ask tough questions of the nominee and make my decision after I have reviewed all the facts," he said.
Another Democratic senator, Heidi Heitkamp of North Dakota, said she had "some concerns" about Tillerson's relations with Russia but would keep an "open mind."
An ongoing CNN survey of all senators did not find any outright Democratic support Tuesday, but with members away for recess, many offices were slow to respond.
Most Democrats who reacted to the nomination were highly critical of Tillerson and indicated they would vote against him.
"I am deeply troubled by Mr. Tillerson's vocal opposition to US sanctions on Russia following its illegal invasion, occupation and annexation of Crimea, Ukraine, and his close personal relationship with Vladimir Putin," said Sen. Ben Cardin of Maryland, the top Foreign Relations Committee Democrat.
"Exxon Mobil also has a troubling history with climate science and the environment. Mr. Tillerson has demonstrated he knows the corporate world and can put his shareholders' interests first, but can he be a respected secretary of state that puts the national security interests of the American people first? It remains to be seen," Cardin added.
Senate rejection of presidential Cabinet picks are rare. Only nine times in history has it happened, according the Senate Historian's Office. The last nominee to be turned back was Oklahoma Republican Sen. John Tower -- who was President George H.W. Bush pick to be defense secretary in 1989 -- amid allegations of heavy drinking.
"Today's criticism and questions may decrease, as senators learn more about the nominee. Some voicing concerns have also stated that they want to hear Rex Tillerson's answers to questions, especially in hearings," University of Richmond law professor Carl Tobias told CNN. "My sense is that Rex Tillerson will probably be confirmed."
While a handful of Senate Republicans -- including Rubio, John McCain of Arizona, Lindsey Graham of South Carolina and James Lankford of Oklahoma -- have gotten heavy attention for their early statements of concern about Tillerson, other GOP senators who are on the committee and who have been critical of Trump were more upbeat about the Exxon chief.
"The fact that former secretaries of state James Baker (and) Condoleezza Rice, and (former Secretary of Defense) Robert Gates are recommending Mr. Tillerson carries considerable weight," said Sen. Jeff Flake, R-Arizona.
And Sen. Rand Paul, R-Kentucky, who is highly interested in the operations of the State Department, said Tuesday he was "keeping his mind open" to supporting Tillerson.