Here's the surprising thing - many people, in principle, agree with the LP or at least with major parts of it. The problem isn't the philosophy - elections in the US aren't about philosophy, they're about issues and there is a great gulf of difference between the two. Libertarians lose on the issues, not on philosophy. This is because people weight issues and the two majors tend to cover the space of issues that people actually weight heavily.
The problem is with a lack of acceptance of the philosophy. If it were widely accepted, libertarians would either heavily influence one of the major parties or be a powerful force on their own.
Third parties do not have to, and in fact cannot, operate on different issues than the major parties. The issues are the issues. The key to a party is a coherent blend of positions on the issues.