Chuck Purgason is a long, longggggggggggg shot for the Senate nomination in Missouri but there is one thing he has on his side: Congressional Republicans are not that popular even with the GOP base in the state. Only 44% have a favorable opinion of them with 38% seeing them unfavorably. If they continue to become more unpopular and Purgason can effectively frame Blunt as emblematic of the problem that may be his one and only shot.
If you look at where Blunt and Purgason are drawing their support right now, it looks to be much more a pro-Washington vs. anti-Washington thing than a moderate vs. conservative thing. Among conservatives Blunt leads 55-13 and with moderates he's up 46-23, an indication that Purgason is not picking up much of his support from people concerned about Blunt's ideological purity- perhaps the opposite actually, that Purgason is benefiting from people who think Blunt is too conservative.
There's a bigger divided based on how people feel about Congressional Republicans. Those who like them give Blunt a 62-13 advantage. Those who dislike them give him only a 47-20 lead. If there is a winning message for Purgason that's it-how are we going to clean up the mess in Washington with someone who's been causing the problem for the last 13 years?