After handing Obama a Red Sox jersey with No. 44 on the back, Ortiz grabbed his phone and took a picture of the two of them.
"Big Papi selfie," Obama proclaimed.
For Ortiz, making himself at home on a stage with the commander in chief just seemed like the natural thing to do.
"You don't get that opportunity every day to chat a little bit with the president and take a selfie with him," Ortiz said.
It was the third championship trip to the White House for Ortiz, but the first for many others, including Jonny Gomes, who wore a suit jacket designed like an American flag.
Gomes also brought one of those jackets as a gift for the president, signed by all the players.
"He approved," said Gomes. "He made sure to tell me he liked it. He thanked me for his, and the team for signing it. He definitely approved. He made sure to look me right in the eye and said, 'Nice jacket.'"
For the Red Sox, who had an off-day on Tuesday in the midst of a three-game series in Baltimore, this was a day of celebration and enjoyment.
"This has been a great experience once again," said manager John Farrell. "We've got a couple of guys here who have been fortunate enough to do this multiple times. To share another great moment built upon 2013, this has been a great day."
Despite his proud status as a White Sox fan, Obama proved plenty knowledgeable when it came to those other Sox.
"Now, I thought I invited the Red Sox here today, but there must be a mistake because I don't recognize all these clean-shaven guys," Obama said in his opening remark. "There's one guy -- a couple guys who decided they thought the beard was working for them. But beards or no beards, it is an honor to welcome the 2013 World Series champion Boston Red Sox to the White House."
Obama spoke not just of the on-field accomplishments of the 2013 Red Sox, but he also highlighted the way they helped unify the city after the tragic Boston Marathon bombings.
"Obviously, all the wins were sweet for Red Sox fans, but I think for the nation as a whole, there was something about this particular squad that was special and will go down in history -- not just because they went from worst to first, but because they symbolized the grit and the resilience of one of America's iconic cities during one of its most difficult moments," Obama said.
"Nearly one year ago, hundreds of thousands gathered on a beautiful spring day to run and cheer the historic Boston Marathon. But a senseless act of terror turned celebration into chaos, and joy into anguish. Four young people lost their lives. Hundreds were injured. The city was rocked. But under the guiding hand of somebody who I consider one of the finest public servants that America has known, Mayor Tom Menino of Boston, who is here today, and his lovely wife, Boston stood resolute and unbowed and unbroken.
"And as the smoke cleared, we gained inspiration from the injured who gamely tackled their recovery -- those who are running and walking again, including the young woman who has returned to professional dancing with a prosthetic leg. And we took heart from the first responders who put their lives at risk and bravely ran toward danger -- people like Officer Richard Donahue of the MBTA Transit Police, who was shot and nearly killed that night. After months of rehab, Richard is walking again and keeping up with his 18-month-old son, and we're so proud to have Richard here today. Give him a big round of applause."
Obama then made reference to another tragedy that rocked Boston a week ago, when two firefighters lost their lives in the line of duty.
"Today, our hearts are in Boston again," Obama said. "We've got the families of firefighters Michael Kennedy and Lieutenant Edward Walsh, who gave their lives protecting others from a massive blaze last week. And their sacrifice, like the sacrifice of those made last year, reminds us of the selfless courage of everyday heroes who put their lives on the line to help others. The first responders, the brave citizens, the resolute victims of these tragedies -- they're all Boston Strong.
"And ultimately, that's what this team played for last season, and every man behind me did his part to keep the team rolling."
Obama spoke of Xander Bogaerts breaking in last October as the "upstart rookie," of Shane Victorino, "my fellow Hawaiian," and he also mentioned John Lackey, Jon Lester, Mike Napoli, Koji Uehara and, yes, Big Papi.
"And I think Big Papi put it better and more colorfully than any of us could," said Obama. "I won't repeat his quote. But the point is, Boston and the Red Sox were one this season."
In closing, Obama said, "So congratulations to the Boston Red Sox and Red Sox Nation. Good luck this season. May the best Sox win."