Could someone explain to me what law gives the Obama administration the power to make up new gun control regulations?

A federal judge has upheld the Obama administration's ability to impose new reporting requirements on gun dealers. Here is a copy of the original filing by the NSSF. Here is their statement on yesterday's district court ruling.

We respectfully disagree with the court’s reasoning which places our industry on a “slippery slope.” Today’s ruling will allow ATF to demand whatever information it wants from any law-abiding retailer anywhere in the country for any reason ATF wants simply by sending a letter demanding information. While we understand ATF’s motivation is to try to curtail violence in Mexico, Congress simply has not granted ATF regulatory carte blanche. NSSF looks forward to having the Court of Appeals review the district court’s flawed decision. . . .

The main quote that I get from the above filing is this:

In response to the DOJ Office of Inspector General's review of proposed ATF action" seeking a requirement for reporting multiple sales of long guns[,]" the ATF itself questioned its authority to impose such a new legal requirement:

ATF concurred with this recommendation, but noted that it may require a change in the Gun Control Act, which is beyond the ATF's and the Department's authority. ATF stated that it would explore the full range of options to seek information regarding multiple sales of long guns.