Sexton will make his first career start at home on Saturday against North Carolina if Rix, who suffered a high ankle sprain and was on crutches Sunday, is not healthy.
A decision is expected today.
Sexton's teammates were impressed by their quarterback's performance.
He finished 17 of 26 for 162 yards and a long touchdown pass to receiver Chauncey Stovall, the team's first this season.
But the elimination of turnovers and a penchant for keeping drives in motion impressed FSU coach Bobby Bowden and others. Sexton's low-key manner also has made a mark.
"I am laid back myself but not that laid back," team captain Ray Willis said and laughed on Sunday when asked about Sexton's demeanor.
"He's the kind of guy who is very laid-back, calm. Nothing really seems to affect him. Still, you can really tell he loves the game."
Receiver Craphonso Thorpe agreed, say's Sexton's composure was a strength.
"First of all he's here at Florida State so he's capable of getting the job done," Thorpe said.
"It's natural when you first get out there you are going to be jittery. But he settled down very quickly. He and (Chris) are different (in the huddle). Chris is more up-tempo.
"You can't explain it -- he's just pretty laid back."
"I think Weatherford is more prepared because he played under center in high school,'' Bowden said.
Sexton, meanwhile, was happy to make a positive impact
"I was really nervous at first,'' Sexton said Sunday.
"When I finally got some time to think [at halftime], I told myself, `I've been waiting my whole life to do this. I know I can do this. Screw it, let's just go do it.' "
And that he did.
"He's probably not the fastest guy," Willis said.
"But as far as what he can do with the football in his hand, how he handles himself in the pocket and his ability to sidestep the rush and to deliver like a 60-yard bomb with a little flick of the wrist, to me that's impressive athletic ability."
Safety Pat Watkins, who played at rival Lincoln High School and said he intercepted Sexton during the season, also knows how well Sexton is capable of playing.
"He went into that game (Clemson), calm and cool, and just got better and better," Watkins said.
"In practice, we (first-team defensive players) go after him to see what kind of decisions he's going to make. But nothing really seems to bother him. He's pretty mellow."