The dedication of George W. Bush's presidential library on Thursday shines a spotlight on two of the nation's most prominent political dynasties: the Bush and Clinton families — and the prospect of another White House campaign, in 2016, featuring them again.

The two families could be thrust into the spotlight once again if Hillary Clinton or Jeb Bush runs for president in three years. During the 2008 campaign, Bill Clinton served as his wife's top surrogate, vouching for her abilities. In recent days, George W. Bush has encouraged his younger brother to seek the White House, saying in an interview with C-SPAN, "My first advice is: Run."

"We've had enough Bushes. He's by far the best qualified man...but no."

- Barbara Bush, Former First Lady

Playing on the idea of his brother and Hillary Clinton appearing at the library opening, the former president told ABC News: "It'll be a fantastic photo here. It would certainly eclipse the museum and the center."

But first lady Barbara Bush appeared to disagree. Asked in an interview Thursday on NBC's "Today" show how she felt about Jeb Bush running for president, Mrs. Bush said, "We've had enough Bushes."

"He's by far the best qualified man," Mrs. Bush said. "But no."

Recent polling has found an improving assessment of George W. Bush's presidency, a measurement which could play a factor in how Jeb Bush would be viewed in future Republican primaries. A poll released in March of registered Republicans by Quinnipiac University found Jeb Bush trailing GOP opponents such as Florida Sen. Marco Rubio, Wisconsin Rep. Paul Ryan and Kentucky Sen. Ron Paul.

Hillary Clinton remains popular, with a Gallup poll released earlier this month showing that 64 percent had a favorable opinion of her. The former first lady delivered her first paid speech on Wednesday in Irving, Texas since leaving the helm of the State Department earlier this year.

Meanwhile, Clinton spoke the private event to the National Multi-Housing Council's board of directors, a trade group that represents the apartment building industry. Terms of Clinton's compensation for the question-and-answer session were not disclosed, but it was expected to net six-figures.

Tom Bozzuto, chairman and CEO of the Bozzuto Group, a real estate services organization based in Greenbelt, Md., conducted an interview of Clinton during the hour-long session, and said he covered topics such as international affairs, the economy and the role of rental housing in the U.S.

When he asked about 2016, Bozzuto said Clinton told the audience that she was "too freshly released from her role as secretary of state to have time to even think about this." Bozzuto said Clinton said she had been asked about the subject by someone in the hallway minutes before the speech. "She said she was looking forward to having time to relax," he said.

The presidential trail follows both of them three years before the next election. Clinton supporters gathered outside her private speech in nearby Irving, Texas, on Wednesday night while Jeb Bush received encouragement to run for president during a speech at a Dallas civic group. Looking to the future, Jeb Bush pointed to the nascent campaign in Texas of his 37-year-old son, George P. Bush.

"To be honest, I'm focused on the land commissioner race in 2014," Bush said with a smile.

Presidential politics can wait.

Bushes, Clintons and an Obama

President Barack Obama, who broke a 20-year string of either a Bush or Clinton in the Oval Office, will join four ex-presidents at the red-brick library on the campus of Southern Methodist University. Obama has his own back story with the families — he waged a long primary race against Hillary Rodham Clinton in 2008, campaigned vigorously against Bush's policies and then turned to the former senator and first lady to run the State Department. When Obama needed a re-election boost last year, former President Bill Clinton was there to help.

The White House binds the two families — from former President George H.W. Bush, who presided over the end of the Cold War but watched his popularity fade, to Bill Clinton, whose "I feel your pain" message created a connection with Americans that survived impeachment, to the younger Bush, whose bullhorn speech amid the wreckage of the 9/11 attacks in New York was followed by draining wars in Iraq and Afghanistan that left him unpopular in his second term.

"The presidents' club is small," said Mary Matalin, a longtime George W. Bush adviser. "Only presidents who have sat behind that desk in the Oval Office know the weight of it. There's just a bond there that nobody else can understand except for a handful of people who have done it."

The families first squared off in 1992, when George H.W. Bush ran for re-election and faced Bill Clinton and independent H. Ross Perot in a riveting campaign that took place as Bush's sky-high approval dwindled following the first Iraq war.

Clinton repeatedly questioned Bush's handling of the economy while the incumbent challenged the fitness for office of Clinton and running mate Al Gore, punctuated by Bush's claim that his English springer spaniel, Millie, knew more about foreign policy "than these two Bozos."

George W. Bush served as an aide to his father's re-election campaign, giving him a close-up view of his father's defeat — and plenty of reasons to dislike the opponent. But the families eventually formed a connection that was helped by a common understanding of the burdens of the office.

"They both have a real commitment to public service and are willing to take the slings and arrows that go with it," said Paul Begala, a former aide to Bill Clinton.

When the Clintons arrived at the White House in January 1993, aides to both families said the Bush family was gracious to the new president and his family. The elder Bush avoided criticizing his successor and after Clinton's presidency, the two joined forces to raise money for victims of the devastating tsunami in Asia in 2005 and Hurricane Katrina in 2006.

Aides describe a friendship between the two ex-presidents that almost resembles a father-son relationship. Bill Clinton has visited the ailing ex-president at his homes in Houston and Kennebunkport, Maine, and they keep in touch. Former first lady Barbara Bush joked in a 2012 interview with Parade Magazine that her sons refer to Clinton as their "brother by another mother."

Bush 41, as he is known, told Clinton in a 2006 letter that presidential politics might strain their friendship, "but it is my view that it will survive. In any event, I have genuinely enjoyed working with you. Don't kill yourself by travel or endless rope lines."

That friendship helped connect Clinton and George W. Bush, who campaigned for president in 2000 on restoring "honor and dignity" to the White House following Clinton's impeachment over a sex scandal. After Haiti's devastating earthquake in 2010, Obama tapped Clinton and the younger Bush to lead a relief effort.

Joshua Bolten, a former chief of staff to George W. Bush and a board member of the Clinton Bush Haiti Fund, recalled that on their first trip to Haiti, the presidents wore tan baseball caps emblazoned with the number 85 — the combination of the 42nd and 43rd presidents. He said the relationship between Clinton and the elder Bush "helped open the door to a good 42 and 43 relationship."

Both families know what it's like to watch a family member face the scrutiny of a national campaign. Bolten said that during the 2008 race, Clinton and George W. Bush would talk by phone about the campaign as Hillary Clinton sought the White House — a time when Bush's approval ratings sank and Republicans avoided him.

"Both political junkies. One of them very decidedly on the sidelines, the other one engaged but not the principal," Bolten said.

"And having shared the experience of having a loved one running for president or being involved in the arena and being attacked, from their perspective unfairly; I think that was something of a shared experience," Bolten said. "They could definitely relate."

Based on reporting by the Associated Press.