I believe that unprecedented success of Bernie Sanders campaign have shown us that people in the United States want something different. Ten years ago it would be unimaginable that presidential campaign publicly support the idea of any kind of socialism. And look where are we now. I believe that American politics won't be influenced so much by Sanders himself, but rather by his political ideas.
Yes, Sanders will be influential in the coming years. As a strong candidate for democratic nominee for the president of the United States, Sanders has grown a strong voter base which can be used to influence other elections such as those for the House of Representatives and the Senate as well as local elections.
Since Sanders supports a candidate elected in the House of Representatives I'm sure he will have a little more influence in that institution now that they are there. I don't see any reason why he wouldn't have that influence. However it might deped on other candidates and how their elections go.
Bernie Sanders has been one of the most unique presidential canidates of all time, and unlike some people who get there "15 minutes of fame" and then fade into the ether, he has proven his worth and his value. He is likely to contiute to fight for what he believes in and his supporters will be influenced by him.