If a federal officer claims you lied to him, you can be arrested and charged with the crime of making false statements. You do not have to make the statements under oath (which would be the different charge of perjury).
This statute – which is referred to as Section 1001 and which can be read here in all its prolix glory — is the reason why Martha Stewart has a Bureau of Prisons number.
The only way to immunize yourself against a false statements charge is to refuse to speak to federal officers.
“Wait,” you ask, “what about telling the truth?” Doesn’t work. If, in the course of your conversation, you mis-remember something or speak inarticulately, you can now be arrested. Innocent mistake? Prove it in court after being jailed, charged, tried and paying for a lawyer.