How influential are the libertarian party in US Politics?

Little to no power; the libertarian movement within the Republican party shares many beliefs with the 3rd party, so their electorate and views are represented. Many of the leaders of the Libertarian party were former Republicans, such as Ron Paul (Texas Congressman), Gary Johnson (New Mexico Governor) and Bob Barr (Georgia Congressman) Their biggest success, and which they got the largest percentage of votes, was in 2016, when they got 3.27% of the vote.