Even without the Second Amendment, the federal government would still have very little power to regulate guns.

Many founders argued that there wasn’t even a need for a Bill of Rights because the federal government can only do things it is specifically authorized to do by the Constitution. If a power isn’t there, it can’t exercise it. And there is no power to regulate firearms.

“It has been said that in the federal government they are unnecessary, because the powers are enumerated, and it follows that all that are not granted by the constitution are retained: that the constitution is a bill of powers, the great residuum being the rights of the people; and therefore a bill of rights cannot be so necessary as if the residuum was thrown into the hands of the government. I admit that these arguments are not entirely without foundation; but they are not conclusive to the extent which has been supposed. It is true the powers of the general government are circumscribed; they are directed to particular objects; but even if government keeps within those limits, it has certain discretionary powers with respect to the means, which may admit of abuse to a certain extent, in the same manner as the powers of the state governments under their constitutions may to an indefinite extent; because in the constitution of the United States there is a clause granting to Congress the power to make all laws which shall be necessary and proper for carrying into execution all the powers vested in the government of the United States, or in any department or officer thereof; this enables them to fulfil every purpose for which the government was established.”
James Madison, speech on the House floor as he introduced the Bill of Rights

For Further Reading

Constitution 101: Bill of Rights

Thirty Enumerated Powers

Tenth Amendment: The Enumerated Powers of the States

Financial Writer Gets F as Second Amendment Expert

Mike Maharrey