Yes, you can go to jail just for lying to federal agents. See this article:
How to Avoid Going to Jail under 18 U.S.C. Section 1001 for Lying to Government Agents
http://library.findlaw.com/2004/May/11/147945.html
Excerpt:
Title 18, United States Code, Section 1001 makes it a crime to: 1) knowingly and willfully; 2) make any materially false, fictitious or fraudulent statement or representation; 3) in any matter within the jurisdiction of the executive, legislative or judicial branch of the United States. Your lie does not even have to be made directly to an employee of the national government as long as it is "within the jurisdiction" of the ever expanding federal bureaucracy. Though the falsehood must be "material" this requirement is met if the statement has the "natural tendency to influence or [is] capable of influencing, the decision of the decisionmaking body to which it is addressed."
(Ironically, the government lies to us all the time, but there are apparently no penalties for that.)