“That’s beautiful,’’ Obama said twice.

Giants fans could utter the same words amid a moment they dreamed of seeing: Their castoffs and misfits standing on risers in the East Room of the White House accepting congratulations from the president on winning the 2010 World Series.

Yesterday’s 25-minute ceremony was a first for the franchise. President Eisenhower did not do this when the Giants last won, in 1954.

In front of about 200 Giants investors and their families, and a Who’s Who of political leaders with ties to Northern California, Obama had some fun with the champs, only appropriate for a group that has parodied itself.

“Then there’s the guy with the beard,’’ Obama said as he turned to Brian Wilson in the back row. “I do fear it.’’

Obama also noted that nine teams bypassed Tim Lincecum, before the Giants selected him in the 2006 draft, fearing his body would “fly apart’’ because of his thin frame and whip-like delivery. Lincecum then proved them wrong by winning two Cy Young awards and a World Series ring.

“America learned sometimes it’s a good idea to bet on the skinny guy, so you and me,’’ the lithe president said to laughter from Lincecum and the crowd.

The champions’ visit to the White House may have been a political cliché, but it remains a big deal for the teams that win, especially those that do not win often.

Bochy said in a text after the ceremony that he and the president discussed baseball, golf, and Bochy’s roots during a private chat.

“When I was walking down with him,’’ Bochy said, “I was thinking of all the presidents making the walk to the East Room for all those world-changing press conferences, and we were making the same walk.

“He’s got a great sense of humor.’’

Which he showed in suggesting that his own favorite team was still in the playoff hunt despite evidence to the contrary in the standings.

“I want to wish the [Giants] luck the rest of the season, unless the White Sox are in the Series,’’ Obama said. “Right now, that’s not a sure thing.’’

On Wilson, the president said, “Underneath Brian’s beard, and the Spandex tuxedo and the sea captain costume and the cleats with his face on them, is also one of the most dominant closers in baseball.’’

Actually, Wilson wore a natty blue pinstripe suit. This was not the ESPYs, though it did seem like a sporting event momentarily after the Giants entered the room. An uncomfortable silence that permeated the room before Obama entered was broken by someone yelling, “Take three in Philly!’’ Which emboldened another person to yell, “Where’s the Machine?’’

And yes, there was one “Beat LA’’ chant.

The biggest cheers and longest ovation went not for the current Giants nor Obama, but for Willie Mays, who was introduced like so many foreign dignitaries who visit the White House.

Obama had fun with the “Say Hey Kid’’ at his own expense as he recounted his trip to the 2009 All-Star Game on Air Force One, with Mays on the flight as Obama’s guest.

“It was an extraordinary trip,’’ Obama said. “Very rarely when I’m on Air Force One am I the second most important guy on there. Everybody was just passing me by [and saying], ‘Can I get you something, Mr. Mays?’ ’’

More applause greeted the president’s acknowledgement of the Giants’ deeds in the community. He specifically cited Barry Zito’s “Strikeout for Troops’’ and the Giants being the first team to support publicly “It Gets Better,’’ a campaign against bullying, particularly targeting gay youth, in hopes of stemming suicides.

“So that’s what this team is about - characters with character,’’ Obama said. “Even though this team is a little different, even though these players haven’t always followed the traditional rules, one thing they know is how to win.’’