(AP) -- Donald Trump is inviting a clash in a narrowly divided Senate by selecting Rex Tillerson for secretary of State despite well-publicized concerns from several GOP senators over his ties to Russia.

The likely confirmation fight could be an early test of Trump's sway over Congress, and demonstrate how much appetite there is among Republicans to stand up to their president.

For now, three Republican senators have publicly voiced concerns about the Tillerson nomination: Sens. John McCain of Arizona, Lindsey Graham of South Carolina and Marco Rubio of Florida. All have cited the Exxon Mobil executive's history of making deals in Russia and his close ties with Vladimir Putin, which include opposing sanctions sought by the U.S. and Europe against Russia after it invaded Crimea.

However, none of the three has said thus far that he will oppose Tillerson. And only Rubio sits on the Senate Foreign Relations Committee, which will hold a confirmation hearing in early January to consider the nomination.

"While Rex Tillerson is a respected businessman, I have serious concerns about his nomination. The next secretary of state must be someone who views the world with moral clarity, is free of potential conflicts of interest, has a clear sense of America's interests, and will be a forceful advocate for America's foreign policy goals," Rubio said. "I will do my part to ensure he receives a full and fair but also thorough hearing."

The committee currently has 10 Republican and 9 Democratic members, meaning Tillerson needs support from every Republican to get a successful committee vote, presuming Democrats all oppose him. Yet even if the panel rejects him, there is precedent for the full Senate to take up his nomination.

The Senate will be divided 52-48 in favor of the Republicans next year, meaning Tillerson could lose only two Republicans if all Democrats voted "No." That scenario would produce a 50-50 split and require a tie-breaking vote from Mike Pence, who by then will be the new vice president.

It's also possible, though, that Tillerson could garner support from one or more of the moderate Democrats.

The last time the Senate rejected a presidential Cabinet pick was in 1989 when it voted down John Tower as George H.W. Bush's defense secretary after he had already been rejected by the Armed Services committee. More frequently, nominees have withdrawn from consideration when opposition built, as happened in 2009 with Tom Daschle, President Barack Obama's first pick for Health and Human Services secretary.

It was unclear Tuesday whether the fight over Tillerson would turn into a major brawl in the Senate or just a minor skirmish. One question is how hard Democrats, who've made clear they want to focus on economic issues, will fight. Several issued statements Tuesday angrily denouncing the nomination, but the Democrats' incoming leader, Chuck Schumer of New York, was more measured, pointing to Tillerson's Russia ties and calling for a thorough and lengthy confirmation hearing "given these serious concerns."

Tillerson immediately picked up support from the top two Senate Republicans, Majority Leader Mitch McConnell of Kentucky and Majority Whip John Cornyn of Texas. McConnell praised Tillerson's "decades of experience" and concluded: "I look forward to supporting his nomination."

The chairman of the Foreign Relations Committee, Bob Corker of Tennessee, who was himself passed over for the job at State, also issued a favorable statement, though without saying how he planned to vote. Several other GOP committee members issued statements praising Tillerson or sounding open to his nomination. Still others were taking a wait-and-see approach, including Sen. Cory Gardner of Colorado, who said: "Congress has the constitutional responsibility of advice and consent and we will rigorously exercise it."

For congressional Republicans and Trump, a major question hanging over their emerging relationship is what steps Trump may take to keep party members in line, and how Republicans will respond in turn. Few GOP lawmakers, especially those up for re-election, want to be on the receiving end of a critical tweet from Trump. The Tillerson confirmation may offer clues to how that dynamic will play out throughout Trump's administration, including when Trump takes policy stances contrary to GOP dogma, such as pushing for stiff tariffs on imports or a massive infrastructure bill.

Electoral considerations may already be playing into lawmakers' posture toward Trump. GOP Sen. Jeff Flake of Arizona, who serves on the Foreign Relations Committee, was one of the most outspoken Republicans against Trump ahead of the election, including challenging him to his face during a Capitol Hill visit in July.

But Flake is up for re-election in 2018 in a state Trump won, and has already drawn a conservative primary opponent. On Tuesday, Flake issued a statement sounding open to Tillerson's nomination, citing his support from former secretaries of State and Defense marshaled by Trump's team.

Backing from former Secretaries of State James Baker and Condoleezza Rice, and former Secretary of Defense Robert Gates carry "considerable weight," Flake said. "I look forward to the hearings."

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Associated Press writer Mary Clare Jalonick contributed to this report.