Republicans before the election worked to convince Libertarians that a vote for Gary Johnson (or any other third party) was a wasted vote -- that Libertarians needed to be voting against Obama and therefore for Republicans. Some libertarians have argued that the only way to change the Republican Party is from within. Libertarians need to join the party and then work to make the party less statist.
I thought this was a crock at the time and think so even more now. Here is the key thought: Republicans are not going to change their platform and their candidates and their positions to woo voters they are already getting. After the election, no one in the Republican leadership was talking about what a mistake it was to run a big government Republican like Romney -- the ex-governor of Massachusetts for God sakes -- who authored the predecessor to Obamacare. No one was wondering about Gary Johnson as a 2016 candidate.
What the GOP did do is panic at the shellacking they got among Hispanic voters. The ink was not even dry on the ballots before Republican leadership was considering abandoning their anti-immigrant stance in order to win more Hispanic voters. I am not sure that will get them Hispanic voters, but whether they are right or not, that is the conversation they were having. They were asking, "How do we attract voters WE DID NOT GET" -- not, "how do we attract voters we are already getting".
The turn of the century Progressive Party (William Jennings Bryant, free silver, etc) never won a Presidential election but both the Republicans and Democrats co-opted many of their platform positions because they sought to attract voters they were losing to the Progressives.
I don't see how Libertarians can look at a party that has fielded John McCain (author of speech restrictions) and Mitt Romeny (author of the proto-Obamacare) as any sort of long-term home. Heck, the Republicans more seriously considered Rick Santorum and Donald Trump than Gary Johnson or Ron Paul. I respect what Mr. Paul has done in bringing libertarian issues to the debate, but as long as he keeps reliably delivering his voters to whatever lame statist candidate the party fields, the GOP is never going to seriously address libertarian concerns.