What webleymkv said above is correct. Does that mean that Obama will not try it? He could try to put in an EO but it would undoubtedly be challenged in court. Unfortunately that could take years to wind through the courts and it would screw gun owners in the meantime. That would give Obama an immediate fix (albeit temporary) and allow the Dems time to work on a real law to screw gun owners.
President Obama would have more in his way than just the courts. An overreaching EO is a usurpation of the power that is delegated to congress rather than the presidency. Even in cases where the usurper is a member of the majority party, congress has historically guarded their power rather jealously when EO's become too overreaching. The jealous guarding of congressional power is wise on the part of congress because allowing a president to overstep his authority sets a precedent for future administrations.
It would not serve congressional Democrats well to allow President Obama to overstep his authority because, while "their guy" may be in the White House now, such will certainly not be the case forever. If Democrats allow the current president to usurp congressional power, they will likely find themselves in an extremely unfavorable position in the future when a Republican is president and "the shoe is on the other foot."
Also, it must be remembered that the Democrat party does not control the entire legislative branch of the government. The Republicans still control the house and I very much doubt that they would take kindly to the president overstepping his authority. Similarly, many congressional Democrats come from politically moderate or conservative districts where gun control remains a losing issue. They're already facing guilt by association for being members of the same party as a president who publicly supports a position unpopular in their district, allowing him to actually act on said position could only serve to hurt their chances for re-election. Remember, Obama may not need to worry about getting re-elected anymore, but congress still does and 2014 isn't all that far away.