But Paul has broken with GOP orthodoxy on a number of national security policies: supporting Obama's decision to normalize relations with Cuba; pledging to end the NSA program by which the U.S. government has collected the phone data of millions of Americans; suggesting the U.S. should engage in direct talks with Iran about its nuclear program; and saying he would oppose U.S. airstrikes in Iraq to fight ISIS, a position he has since reversed.
While polls suggest some younger Republicans agree with Paul, most of the party's members in Congress adamantly oppose these positions, isolating the Kentucky senator within the GOP.
Nearly all of his 2016 rivals are to the right of Paul on foreign policy. Two potential candidates, South Carolina Sen. Lindsey Graham and former United Nations Ambassador John Bolton, have said they are considering running for president to show the Republican Party remains committed to a strong national defense, even though Bolton and Graham have almost no chance of winning.
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Former congressman Mike Rogers, once chair of the House Intelligence Committee, is now leading a political committee devoted to promoting hawkish national security views in early primary states like Iowa.
All of these moves are directed at preventing Paul's views from taking hold within the broader Republican Party.
Paul is now trying to reposition himself on defense issues, even unsuccessfully pushing a bill last month in the Senate that would have increased defense spending.
But these shifts may have come too late. Many influential Republicans, like Sen. John McCain of Arizona, have sharply criticized Paul's national security stances and would likely back a number of the other 2016 candidates before they considered the Kentucky senator. McCain himself, in a interview two years ago with The New Republic, wouldn't answer when asked if he would back Paul or Hillary Clinton in a hypothetical presidential contest.
Paul also faces three other major challenges. First, his father Ron, the former Texas congressman and perennial presidential candidate, remains around the periphery of national politics, often making controversial remarks.
The small but fervent coalition of supporters that Ron Paul built was a huge factor in Rand Paul being elected in Kentucky. And his father's devotees coffer the younger Paul a natural network of both donors and voters for his 2016 campaign.
But in the same way that Jeb Bush inherits some of the perceptions of his brother's flawed Iraq policy, Rand Paul must deal with the negative impressions his father left during his presidential campaigns. And Paul's father made some huge political blunders, such as the newsletters with demeaning comments about African-Americans that went out under Ron Paul's name during the 1980's and 1990's.
And while Rand Paul is not as libertarian as his father, the younger Paul has taken controversial views that illustrate a deep skepticism about government. Rand Paul was sharply criticized when he said earlier this year that parents should not be required to have their children get measles shots. The GOP is generally a conservative, limited-government party, but not truly libertarian, and Rand Paul's view are at times out of the step with the broader party.
Finally, many Republicans are wary of electing a first-time senator, arguing that Obama suffered from a lack of executive experience.
How could Paul win? It will be important for Paul to make two cases. First, he must figure out a way to explain his foreign policy positions in a way that makes them more palatable to GOP elites and ultimately conservative voters. The candidate has already had a private meeting with Sheldon Adelson, the major GOP donor who is strongly pro-Israel, trying to ensure Adelson does not fund anti-Paul efforts during the primary season.
Second, Paul must convince Republicans that his extensive outreach to the black community over the last two years can translate into votes, making him the most electable of the GOP hopefuls in a general election. Republicans won less than 10 percent of the black vote in both 2008 and 2012, a number Paul has suggested he could increase.
One key advantage for Paul is the primary calendar. Paul's father ran strongly in 2012 in states with caucuses, which reward having intense, organized supporters, and states with a strong libertarian streak. Two of the first four states in the GOP primary process, Iowa and Nevada, hold caucuses. In New Hampshire, another early state, there is enough of a libertarian movement that Ron Paul finished as the runner-up to Mitt Romney in the 2012 primary, getting 23 percent of the vote.
But even if Paul won Iowa and New Hampshire, it's not clear he could win the GOP nomination. There would likely be a strong push for other candidates to drop out so the GOP establishment could turn the race into a one-on-one contest between Paul and an alternative like Wisconsin Gov. Scott Walker or Florida Sen. Marco Rubio.
The Kentucky senator would be an underdog in that scenario, particularly as the campaign moved to more hawkish states like South Carolina and those with more liberal Republicans, like Florida and Michigan.