Rand Paul's balancing act: What to do with Ron Paul's legacy?

In 2012, Texas Republican Rep. Ron Paul was a force to be reckoned with in the presidential race. His group of supporters - including many young voters - was limited, but passionate. Though he wasn't considered a serious contender for the Republican nomination, he had a strong showing in both the Iowa caucus and New Hampshire primary, finishing third in Iowa with 21.5 percent of the vote and second in New Hampshire with 22.9 percent.

Now his son, Texas Sen. Rand Paul, is contemplating his own presidential bid. Both men come from the libertarian wing of the party, though Doug Wead, who has worked for both Pauls, calls the elder Paul a "classic libertarian" and the younger one a "practical libertarian."

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CBS News Political Director John Dickerson talks about Sen. Rand Paul's day of meeting with people in New Hampshire -- even though he won't make ...

And while Ron Paul was generally viewed as someone who ran for president to prove a point, his son could be a serious contender for the nomination. What he has to do is navigate the tricky dance of keeping his father's supporters engaged and on his side while attracting a whole other group of voters who might not have given Ron Paul a chance.

"His dad's base is not going to be enough,so he's got to find ways to expand the base and become, if not the favorite of different factions of the party, at least acceptable," University of New Hampshire Political Science Professor Dante Scala told CBS News. "He has to do that in such a way that doesn't make his father's base voters feel as if they're being betrayed or that Ron Paul's legacy is being compromised."

Politics isn't the first arena where Paul has followed in his father's footsteps. Like Ron Paul, who had a medical career that preceded his first run for office, Rand Paul also started out in the field of medicine. He was always active in politics, serving in the Young Conservatives of Texas club during college at Baylor University. He left for Duke University to attend medical school before completing his undergraduate degree, and he opened an ophthalmology practice in Bowling Green, Kentucky, after he completed his residency.

All the while, though, Paul was helping his father with his congressional campaign and 2008 presidential bid, and he started a group called the Kentucky Taxpayers Union in his home state. His rise coincided with the rise of the tea party in 2009, and in 2010 he defeated Kentucky Secretary of State Trey Grayson, the establishment pick for Kentucky's vacant Senate seat, to become a senator.

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Sen. Rand Paul (R-Ken.) used old-school filibuster tactics, speaking for 12 hours and 52 minutes to hold-up John Brennan's CIA nomination. CBS Ne...

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Rand Paul's balancing act: What to do with Ron Paul's legacy?