"Public speaking is my enemy," Price said. "That's hard. I'd rather come in with a 3-0 count and the bases loaded in a tie game when you're on the road. Public speaking is tough."
Rookie outfielder Fernando Perez also spoke at the rally and urged Florida voters to get out early in support of Obama.
"There have been too many times that elections have been lost because not enough people voted," said Perez.
Perez said he felt more comfortable with a microphone in his hand than Price.
"I've done that before," Perez said. "They asked if anyone wanted to do it, and everybody said no, so I was kind of there by default, as the rookie. I've done a good amount of public speaking, all in high school. I even acted in school plays.
"It was encouraged at my school, but I haven't done it in a really long time. It's a great apprehension for some people, so it helps in a number ways in life. And I had the words in front of me, so it wasn't [too difficult]."
Approximately 8,000 were in attendance to hear the Illinois senator's speech on various topics. Rays players Jonny Gomes, Carl Crawford, Edwin Jackson and Cliff Floyd also spent time on stage, greeting Obama and chatting privately.
"We spoke to him, and he just told us, 'Congratulations,'" Price said. "He goes home at night and that's what he looks forward to, putting on 'SportsCenter' and watching sports."
"I let him make his rounds and get himself focused," Perez said. "We both went to Columbia, so we briefly talked about the different dorms we lived in. But I tried to not take up too much of his time."
The outing was organized when Erin Woodward, the wife of Major League infielder Chris Woodward and a volunteer with Obama's campaign, appeared during the Rays' clubhouse celebration and invited players to the Tampa event. Floyd, a teammate of Woodward's with the Mets, was a chief recruiter.
"Cliff was like, 'Come on over. It would be fun to meet a guy of that stature,'" Price said. "You really can't pass that opportunity up, whether you like the guy or not. He's definitely an icon right now and will be probably for a long time."
Perez said that the Rays teammates were "really excited" for the opportunity to meet Obama, whose campaign opposes Republican senator John McCain of Arizona. Election Day is Nov. 4.
"I'm really not a political person, but the guy is a pretty amazing man," Perez said. "I've read most of his book. He's an amazing American, an amazing guy to meet. What I'm doing is giving me interesting access to some things I didn't have access to before. I don't think two months ago anyone would have asked me to do this."
Obama, a Chicago native, has said in speeches that he would be pulling for the Philadelphia Phillies when the World Series gets under way, since the Rays bounced his White Sox from the AL Division Series.
But, as the Rays wait for Game 1 of the Fall Classic on Wednesday, Obama attempted to make amends to the pro-Tampa Bay audience.
"I've said from the beginning that I am a unity candidate, bringing people together," Obama said. "So when you see a White Sox fan showing love to the Rays, and the Rays showing some love back, you know we're on to something right here," Obama said.
Obama joked that he was going to get a Mohawk to go along with the Rays, saying, "My political advisers said they weren't sure how that was going to play with swing voters. But I congratulate them."
Obama has already been connected to the World Series in another way. The FOX network agreed to delay Game 6 to accommodate a 30-minute commercial for the Obama campaign. If the series goes that far, the first pitch will be pushed back from about 8:20 p.m. ET to 8:35 p.m. ET.