CEDAR RAPIDS, Iowa — Representative Ron Paul has a message for the ardent followers who read his books with a highlighter and donate to his fund-raising “money bombs” on the Internet: Winning the Iowa Straw Poll next month would “rock the establishment.”

Mr. Paul’s libertarian views have moved from the fringe toward the mainstream of conservative thinking in the past several years, with his warnings about fiscal meltdown gaining new resonance and the 2008 financial crisis allowing him to press his longstanding critiques of the Federal Reserve.

Now, as he again seeks the Republican presidential nomination, he is hoping to show that he can translate the new attention into votes. And his first test is the straw poll next month, where he is hoping he can organize his band of followers into a political machine capable of beating some or all of his brand-name rivals.

Even if he does not win, a strong showing by Mr. Paul could dent the campaigns of other candidates, especially Tim Pawlenty and Representative Michele Bachmann.