My problem is that you are painting with such a broad brush. People are not exclusively pro-gun or anti-gun. There are many shades of grey. I agree Obama is against automatic weapons and high capacity magazines but not against all guns. Action speaks louder than words (or theories) and as blank.cd pointed out, he has passed pro-gun bills. Furthermore, not all democrats are like Feinstein and I have seen Obama clearly support the second amendment on multiple occassions.
Even the NRA will tell you that it is important to ensure mentally disturbed people do not get access to guns so how can you divorce healthcare and gun control?
I don't see how the gun control legislation under discussion in congress is sneaking through the back door. This is the appropriate political process. His executive orders such as "appoint an ATF director" and "allow more studies" do not strike me as anything inappropriate either.
Are all democrats liberals? Does supporting any regulation of guns whatsoever make someone anti-gun? It's these overgeneralizations and us/them rhetoric that gets you push back.