Hardly anyone, probably not even the candidate himself, believes that Ron Paul can win the Republican nomination. But his strong showings in Iowa and New Hampshire have turned him from a marginal figure into major player in Republican politics. For many, a strong but unsuccessful run to be a party's presidential nominee could be used as a basis for a future presidential run, perhaps by becoming vice president first. I think it highly unlikely that Paul will become a vice-presidential nominee, however, because he is too polarizing. Moreover, at age 76, this is likely to be his last run.
Is there any hope that the Republican candidate, should he win the presidency, will offer some sort of post to Paul? Should he? Paul represents an unusual constituency, a small but dedicated group who differ from Republicans in general on a number of issues. Every political party is composed of diverse interests, but libertarians present a special set of challenges to incorporate into the party mainstream. Unlike another small but devoted following, the avidly pro-life section of the party, libertarians are not single-issue voters. There is not even a major issue most frequently identified with them; instead, their views are relevant in nearly every political action. And while most libertarian views are congenial to most Republicans, there are some views that are so far out of mainstream conservatism that they alienate many potential voters -- issues like drug enforcement and foreign policy, for instance. It is therefore possible for a Republican candidate to say many things that libertarians approve of, but to have a single libertarian in a Republican administration is likely to attract enormous criticism from both Republicans and Democrats.
Still, you don't want to write off the support of this important group of people. Even if a third party is not likely to rise up any time soon, just having libertarians stay home could mean defeat for a lot of Republicans in close races. I have even heard of people identifying themselves as "liberal-tarians," libertarians who somehow believe that the Democratic party represents their views better than Republicans. I find this absurd, but I have to admit that the way Republicans often behave while in office, I can understand why libertarians would be anxious to find an alternative.
So could a Republican president find a place for Ron Paul in his administration? The department of state can be a refuge for a politician out of step with the main line of opinion in his party, as when Colin Powell served there for George W. Bush. In Paul's case, however, this is out of the question. Paul is such an isolationist that his appointment would alienate everyone, including, probably, our allies. Most other cabinet -level positions would almost be contradictory for Paul to hold. Labor? He'd probably want to get rid of it. Energy? Likewise. Housing and urban developement? Same. It is hard to imagine someone with Paul's long and consistently-held beliefs taking over the administration of a department that he doesn't think serves a legitimate purpose. (I'm thinking of Leon Panetta's sudden shift to a defense hawk after his appointment as secretary of defense; I'm not suggesting that Panetta is insincere, but his political philosophy is considerably more flexible than Paul's.) I suspect that he would decline the position, even if offered.
There is one possible alternative, and that is the department of the Treasury. It is true that Paul's website calls for a 0% tax rate, which is one of the things that makes it impossible for Paul to win national office. However, it seems that even he must admit that the government needs to collect some revenue; and since the Treasury was one of the original three cabinet departments, he can't claim that we have ever done without it. Assuming that he would continue to enforce existing laws while promoting their repeal, Paul would make a strong advocate for decreased federal spending as Secretary of the Treasury. He would be a strong advocate for taxpayers, and you can bet he would make the IRS less aggressive in its collection methods and less exacting in its rules.
A president would have to have strong assurance from Paul that he would actually enforce existing laws, because his appointment to such a position would have to excite some fears that he would just refuse to collect money; and while I'm pretty sure he wouldn't do that (or would refuse the position if it was contrary to his conscience), you would want some public statements to that effect at the time of his appointment to calm financial markets. There is always the chance that he would not be approved, and that kind of split with libertarians would be far worse for Republicans than simply leaving Paul to the side. On the whole, I think the risks of appointing Paul to any cabinet position make it very unlikely that a president would take the risk, but I can think of worse people to hold the office.