Pausing, Bush quipped in a low voice: "I know how he felt."
Bush was cheered and applauded by his supporters, who rose to their feet five times during the 15-minute ceremony.
When a red drape was removed from his portrait, the president cocked his head to view the finished work with his hands on his hips. He shrugged.
The 43d president called the work by Alabama artist Mark Carder "a really fine job with a challenging subject."
Bush is the 23d president included in the club's renowned presidential portrait collection, which includes one Democrat (Andrew Jackson, the seventh president) and all but two Republicans (Benjamin Harrison, the 23d president, and Warren G. Harding, the 29th).
"I'm keeping good company," Bush said.
The portrait, underwritten by Union League members Bruce and Eileen Hooper, shows Bush in the Treaty Room of the White House.
Bush is the first president since Herbert Hoover to have his portrait unveiled at the Union League while in office.
In his remarks, a relaxed and playful Bush acknowledged the presence of Republican Sen. Arlen Specter in the front row of the hall.
"It's been a joy to work with you," Bush told Pennsylvania's senior senator, "most of the time."
Of his mother, Barbara, who was recently released from a hospital, Bush told the audience that she is "a tough old bird" who was recovering.
In a more serious moment, Bush said that when someone asked him what it was like to be president, he responded, "Some days you're happy. Some days you're not so happy. And every day you're joyous to serve the United States."
Bush also received the Union League's Gold Medal, one of only 37 recipients since 1863. Others include Vice President Cheney and former Bush cabinet members Donald Rumsfeld and Tom Ridge.
Bush, however, said he was "especially proud to be a co-recipient with a guy I call '41,' " - his father, former President George H.W. Bush, who was presented the medal in 1987.
In his two terms in office - and two turns as a candidate - Bush has been a frequent visitor to Philadelphia. Yesterday's stop was his 15th in the city and third appearance at the Army-Navy game.
He flew into the Philadelphia International Airport by following a game-day tradition of dipping the wing of Air Force One over Lincoln Financial Field.
Other pregame pageantry and traditions revved up the crowd of 69,144. After elite Army and Navy parachute teams landed at midfield, Navy pilots in F/A 18 Hornet jets flew over the stadium, followed by Army pilots maneuvering two Blackhawk and two Apache helicopters.
As the Army squad ran onto the field for the game, it delighted fans and cadets by wearing a new camouflage-style uniform.
"They make our guys look really mean," said Jonathan Medina, a West Point cadet.
As commander-in-chief, Bush showed no favorites before or during the game. He gave both teams the same pregame pep talk in their locker rooms and spent the first half of the game sitting with Army fans, switching to the Navy side at halftime.
As spectators chanted, "U.S.A., U.S.A.," Bush strode to midfield with Defense Secretary Robert M. Gates for a ceremonial coin toss. On the way, Bush spied a football on a tee from practice and, unable to resist the temptation, gave it a good boot for 15 yards to the delight of the crowd.
Mayor Nutter enjoyed the fabled football rivalry in person for the first time yesterday. Standing in an end zone, he said he hoped the city kept the game here. Philadelphia, which has hosted 81 matches, will be the site of next year's event and is seeking to host it after that.
As Nutter took in the scene - the midshipmen in their gleaming white hats, the cadets in their steel-gray topcoats, cannons fired for touchdowns - he said, "These are great young people who love their country."
"It's reassuring to know that even with all the conflict around the world, we can still enjoy this great tradition."
Contact staff writer Jennifer Lin at 215-854-5659 or firstname.lastname@example.org.