For those who are complaining the President has exceeded his Constitutional authority by circumventing the legislature, irony alert: The Executive Order is the quintessential act of the President fulfilling his Constitutional responsibility under Article II to exercise the "executive power of the United States." An Executive Order is simply an instruction from the head of the Executive Branch to the relevant personel under the authority of the President pursuant to Article II on how to execute the laws passed by Congress or how to fulfill existing regulations authorized by Congress or how to implement some other Administrative function. Usually these are quite dull things, such as an Excutive Order directing the General Services Administration to establish an "Innovation Fellows Program." Sometimes these have broad policy implications, but are still just instructions on how the President wants the agencies under his authority to act, such as this Executive Order on Using Behavioral Science To Better Serve The American People.
Keeping this in mind, lets review what the President actually did as his Executive Action on gun control.
Here is the fact sheet on the actions the President directed the agencies to take: https://www.whitehouse.gov/…/fact-sheet-n
Read it. You will find that it constitutes a communication from the President to his heads of Department to take certain actions with regard to already existing statutes. These involve (a) directing the Department of Justice and the ATF to direct greater general fund resources already allocated by Congress away from other duties and prioritize enforcement of certain existing statutory duties duly enacted by Congress; and (b) issue a clarification with regard to the enforcement of the existing gun licensing statute as to its applicability. This includes reversing previous guidance that had permitted loopholes such as the "gun show" exemption from background checks and to employ a "totality of the circumstances" test to determine whether any individual is in the business of selling guns. That may make individuals unhappy because it is much less certain than a bright line rule -- it may even chill the sale of guns because individuals that are hobbyists are worried that they may now find themselves classified as gun dealers and need federal licensing. But the that's regulation under the Commerce Clause for you.
Now anyone who doesn't like this is entitled to challenge any action by the ATF to enforce the President's directive once the ATF enforces it against them, or to seek a declaratory ruling in a court of the United States that the plain language of the statutes in question forecloses the interpretation given to it by the ATF (as instructed by the President). [Side point, I'm not sure if the ATF actually needs to do a rulemaking or if this is simply giving instruction on enforcement policies that were never formal rules under the Administrative Procedure Act, but lets set that aside for now. The President can certainly instruct the DoJ to spend more money on its database for background checks and to work with the states to facilitate greater cooperation.] Likewise, Congress can pass a law amending the existing law to explicitly foreclose the interpretation given to it by the President. It can also, in the next budget cycle, include a rider explicitly prohibitting the relevant agencies from expending any funds on the instructions outlined by the President. That's the "power of the purse" thing, which is one of the checks the Constitution gives Congress over the power of the Executive.
Far from being unconstitutional, this is *precsely* the way our Constitution works. For those who don't remember their middle school social studies classes, the Congress passes laws, the President carries them out, and the judiciary resolves disputes that arise under those laws or between the laws passed and executed and the limits impossed by the Constitution. Executive agencies are simply officers appointed under Article II to assist the President in carrying out his function of implementing the laws.
In fairness to the Republicans and conservative pundits who don't seem to understand basic Constitutional law or legal theory (as the President remarked, he used to teach this stuff), this current broohaha over Executive Orders resembles the fuss in the Bush Administration over "signing statements." For those who don't remember when Signing Statements were all the rage (and I do mean rage on the part of Democrats and Progresives), signing statements are official statements of the President on signing legislation into law. These are not that common, and are generaly ceremonial in nature on major bills. Ocassionally, however, the President would say as part of his signing statement that he planned to interpret the law in a particular way to avoid a Constitutional problem. Bush invoked this practice more frequently than previous Presidents, and his claims with regard to the Constitutional powers of the President (particularly with regard to national security) reflected a very expansive (and often controversial) interpretation of the War Powers.
Bush's use of signing statements certainly raised a bunch of interesting legal questions from an Administrative Law perspective, such as whether or not they deserved judicial deference in the same way an agency interpretation gets deference, or simply constituted a statement by the Head of the Executive Branch as "this is how I understand what the legislative branch just told me to do, and which parts I think offend the Constitution, so all the folks part of the Executive Branch should understand how I expect them to interpret this." But the reality from a Constitutional stand point was no different from whether the President issued his interpretation of the law in a signing statement on passage or six months later in an Executive Order. It was the President Bush's expansive interpretation of the War Powers and Executive Authority, not the signing statement itself, that raised Constitutional issues.
To conclude, I get that "Executive Order" has now become a trigger word that acts to most folks as a huge distraction -- especially non-lawyers who don't know what an Executive Order actually is and how it works. But Executive Orders are nothing new and are in no way "bypass" Congress -- at least not in a Cnstitutional sense. Executive Orders are directions from the President, the head of the Executive Branch under Article II of the Constitution, instructing the relevant agency heads and other relevant personnel subject to the President's authority under Article II to do something. It is roughly the equivalent of a memo from a company CEO/President to folks in the company on company policy.
The bottom line here is that the President Obama is limited in what he can do under existing law, so he has used his interpretation of existing law to do what he can. Far from a violation of the Constitution, it is the specific job that the Constitution requires him to do as his #1 priority as head of the Executive Branch. Existing constraints on executive action, as always, remain enforceable in the Judiciary, and Congress may, in turn, may perform its core Constitutional function -- legislation adn appropriation of funds -- to reverse the President's action. People should feel free to debate what they think of the policy, but it would be nice if they actually understood how our system of government works.