Rubio did just that on Monday morning ahead of the committee vote, citing deference to the president in selecting his cabinet and Tillerson's "extensive experience and success in global commerce".
However, in a joint statement released Sunday, McCain and Graham said that while they still have concerns about Tillerson, they believe he will be "an effective advocate for USA interests" and they will therefore vote in favor of his confirmation.
Members of the panel voted along party lines, 11-10, to back Tillerson following a contentious confirmation hearing almost two weeks ago that stoked concerns he might not win the panel's recommendation...
The crowd chanted and held signs before several of Rubio's staffers walked outside and collected letters from the demonstrators.
Sen. Ben Cardin of Maryland, the top Democrat on the committee, said he opposed Tillerson's nomination because "the fundamental role of a secretary of State is to promote American values".
Earlier in the day, Rubio wrote a lengthy Facebook post explaining that he would vote for Tillerson: "Given the uncertainty that exists both at home and overseas about the direction of our foreign policy, it would be against our national interests to have this confirmation unnecessarily delayed or embroiled in controversy". Rubio asked Tillerson if he would label Vladimir Putin a "war criminal" over the Russian campaign in Syria. He added that he hopes the committee does not adopt a policy of asking for nominees' tax returns in the future "because most of those are used for gotcha questions".
Rubio, McCain and Graham all belong to the hawkish wing of the Republican Party, with views that have been mainstream in the GOP for many years.
Republicans work to eliminate the Affordable Care Act and Pre-Existing Conditions Clause
President Trump and Republicans in the Senate and House of Representatives are moving ahead with plans to repeal Obamacare . He said the Affordable Care Act needs to be replaced by something that would "heal" the American people, not harm them.
But at the end of his written statement, Rubio added a note of warning: "Upcoming appointments to critical posts in the Department of State are not entitled to and will not receive from me the same level of deference I have given this nomination".
The oil tycoon with strong ties to Russian Federation was chosen by Donald Trump for the top job.
Monday's committee vote on Tillerson came amid a push by Republicans to swiftly confirm Trump's nominees.
In the days following Trump's announcement that Tillerson was his choice for the job, McCain, Graham, along with Sen.
The Senate planned to spend up to six hours Monday debating the nomination of Rep. Mike Pompeo (R-Kan.) to head the Central Intelligence Agency before voting on him Monday night.
"So many times he qualified (his responses) that he sounded like a business person and not like a secretary of State", Cardin said. As of last week, it didn't appear to being fazing him.