Story highlights Rubio now finds himself with significant leverage over Trump, his former rival

GOP aides were confident Tuesday the handful of GOP critics of Tillerson would eventually support him

Washington (CNN) Secretary of state nominee Rex Tillerson's difficult path to confirmation will begin early next month in the Senate Foreign Relations Committee's hearing room, where one Republican's "serious concerns" about the ExxonMobil chief executive's close ties to Russia could sink his nomination before it even gets to the Senate floor.

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.

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