TIME magazine is the latest national mainstream media outlet to focus attention on Kentucky Sen. Rand Paul‘s efforts to raise his national political profile, devoting four pages to the topic in the latest issue.

Paul, 50, has won exactly one election in his life, but his sudden star power suggests it may be wise to listen to him now. After a month marked by an audacious 13-hour filibuster and his victory in a conservative straw poll, he has vaulted from quirky rabble rouser to GOP agenda setter. From Iowa to Israel, a man just three years removed from his Bowling Green, Ky., ophthalmology practice is laying the groundwork for a presidential bid, and the party can’t afford to ignore him.

One reason is that Rand Paul is not his father. The libertarian agenda of Ron Paul’s presidential bids drew a following as narrow as it was zealous. The younger Paul seems determined to broaden his father’s base of perhaps 10% to 15% of the GOP electorate and is hunting for new recruits across the political spectrum. That means freshening up his dad’s familiar message and downplaying hoary crusades like the gold standard and auditing the Federal Reserve. It means policy surprises, like his outline of a path to legal status for undocumented immigrants. And it means a stage sense and media savvy his father lacked.

But Rand Paul’s rise hasn’t come without friction. Many party elders doubt the Paul family brand is the solution to their identity crisis. GOP hawks are dismayed by his critiques of Barack Obama’s drone policies, not to mention Paul’s calls to curb foreign aid and shrink the U.S. military’s footprint overseas. His blueprint for balancing the federal budget in five years through massive spending cuts and fewer federal agencies won just 18 GOP Senate votes. When Republican colleagues John McCain and Lindsey Graham tore into Paul for showboating on the Senate floor, they said publicly what others mutter in private.