As someone who has taught both administrative and constitutional law at the university level for several years, those who do not believe that Obama has the power to seriously affect legal importation of ammunition, arms, parts kits, etc. are too sanguine about the real limits of presidential power. Generally speaking, the courts will not save you from such.
As noted by several commentators, it is true that under a hierarchy of laws, ie, the Constitution is greater than treaties, treaties are greater than statutes, and statutes are greater than executive orders/agency regulations, and executive orders/regulations are greater than agency policy statements. However, in application, the presumption in court is that the president's or agency's actions are constitutional and lawful unless proven otherwise. If you want a good overview of how the courts have handled executive orders, see Phillip Cooper's book, By Order of the President.
Additionally, most congressional laws are writtenly vaguely so as to cover unforeseen circumstances (and because of disagreement about wording). Agencies may not disobey specific congresssional provisions but courts will generally defer if the agency action is in a gray area. This leaves the agency such as the BATF broad discretion regarding technical aspects as courts will defer to the administrative agency on a technical question such as what is a semi-automatic design that could be easily converted to an illegal automatic one under the NFA (see Chevron v. NRDC or Vermont Yankee for an explanation of this Supreme Court Doctrine). Another example, would be whether or not a particular firearm such as Saiga shotguns have a valid "sporting" purpose would be a technical question that the courts would defer to the ATF. Any legal challenge of an ATF action must generally demonstrate through evidence that the ATF behaved arbitrarily and capriciously in their actions. For a good overview, see this recent 9th Circuit case,
http://cdn.ca9.uscourts.gov/datastore/uploads/guides/stand_of_review/IV_Review_AD.pdf (Parts IV pages 1-8).
Now, what complicates the picture is that judicial deference only applies to technical questions but not legal interpretation of what congressional laws, treaties, or the Constitution means when applying the law to a specific set of facts. Thus, multiple circuits, including most recently the 6th Circuit, have now held that the grandfathering of drop in sears violates the National Firearms Act (
http://www.firearmscoalition.org/in...-reversed&catid=19:the-knox-update&Itemid=144). In this case, the circuit court ruled that any automatic firearm that has not be demilled to BATF standards is an illegal firearm whether or not the BATF has decided to grant an exception. The court has ruled that grandfathering by excluding previously manufactured items before the BATF ruling in 1981 violates the NFA. Thus, the BATF's interpretation of its authority to grandfather under the NFA is illegal.
Similar judicial deference usually obtains for Presidential actions regarding imports and exports. Banning the importation of AK's during the Bush I administration by executive order is one example of how broad presidential import and export powers can be as Congress has written statutes granting broad powers and administrative discretion to the president over these matters.
If Obama truly wants to expend the political capital, he can make life miserable for gun owners, firearms dealers, and importers. He can't ban guns by executive order but he can make them more expensive and discourage ownership by new paperwork barriers, raise compliance costs or even ban imports from some countries under laws that have nothing specific to do with firearms. For example, imports from Russia and other countries could be cutoff using a variety of human rights treaties, the UN Small Arms treaty, financial treaties, or even a failure by Russians to hand over Snowden. What you to determine the limits on agency and presidential action would need to do is a thorough reading of applicable statutes, applicable treaties, and any court interpretations of said statutes and treaties.
Sorry for the long post but it is not a clearcut issue and administrative law makes constitutional law appear simple.