Yes, but never for owing taxes. The IRS can criminally prosecute you and possibly put you in jail if you voluntarily and deliberately violate a known legal duty in order to avoid paying taxes. That would be tax fraud (sometimes called evasion). However, if you do everything right, and find yourself in a bind because you can not pay a tax, you will have collections problems but you will not go to jail.
Tax fraud is the deliberate and willful attempt to evade tax law or defraud the IRS. Fraud, as defined by the IRS, “Is the deception by misrepresentation of material facts, or silence when good faith requires expression, which results in material damage to one who relies on it and has the right to rely on it. Simply stated, is the obtaining something of value from someone else through deceit,” IRM 184.108.40.206.
The criminal fraud penalty requires the IRS to prove intent and this penalty is 100% of the tax owed plus interest. Because intent can be difficult to prove, in many smaller cases the IRS will often opt to assess a Civil Fraud Penalty instead. The Civil Fraud Penalty is 75% of the tax owed, plus interest. Imposing a penalty for Civil Fraud is much easier for the IRS to impose and generally results in the same outcome; to punish an infraction and encourage future compliance.