The legal requirement to hand over the returns is found in 26 U.S. Code § 6103:
(f) Disclosure to Committees of Congress
(1) Committee on Ways and Means, Committee on Finance, and Joint Committee on Taxation
Upon written request from the chairman of the Committee on Ways and Means of the House of Representatives, the chairman of the Committee on Finance of the Senate, or the chairman of the Joint Committee on Taxation, the Secretary shall furnish such committee with any return or return information specified in such request, except that any return or return information which can be associated with, or otherwise identify, directly or indirectly, a particular taxpayer shall be furnished to such committee only when sitting in closed executive session unless such taxpayer otherwise consents in writing to such disclosure.
Enforcement is found in 26 U.S. Code § 7214
(a) Unlawful acts of revenue officers or agents Any officer or employee of the United States acting in connection with any revenue law of the United States—
(3) who with intent to defeat the application of any provision of this title fails to perform any of the duties of his office or employment; or
shall be dismissed from office or discharged from employment and, upon conviction thereof, shall be fined not more than $10,000, or imprisoned not more than 5 years, or both. The court may in its discretion award out of the fine so imposed an amount, not in excess of one-half thereof, for the use of the informer, if any, who shall be ascertained by the judgment of the court. The court also shall render judgment against the said officer or employee for the amount of damages sustained in favor of the party injured, to be collected by execution.
These punishments are essentially identical to those in Section 7213, which describe the punishments for those who unlawfully release returns. I've seen that section quoted in some articles as the basis for punishing failure to provide requested returns to the Chair of the House Ways and Means committee, but I'm not really seeing how that section covers non-compliance. Non-compliance seems only covered by Section 7214, which requires the "intent to defeat" (or various other issues, such as not disclosing known violations to the Secretary, etc.). That may be hard to prove in this scenario, and part of the stalling by Mnuchin may in part because they are exploring if they can build a strong case that it wasn't his intent to defeat the title. The quote of his you note is particularly on point on this, as he explicitly says he intends to obey the law; he's just questioning the constitutional issues involved.