They only defined themselves as "fans of the Constitution," which I am naïve enough to hope includes most of the US. And from scanning some comment threads (I have been away from FB a looong time since joining the group, and am already second-guessing my return) the opinions and positions seem pretty diverse.

The thing is, if people were saying, "Obamacare is unconstitutional because of Article X, Section y," I could respect that whether or not I agreed. My problem is that the posts routinely take it for granted Obamacare, raising the debt ceiling, or [your pet conservative issue here] is automatically unconstitutional, and urge everyone to petition their Congressmen against it. REASONS and EXPLANATIONS, much less citation of the document in question, are virtually never offered; it is simply a matter of "all liberal policy is unconstitutional, therefore supporting the Constitution automatically requires opposing all liberal policies." Beyond the Houses power to introduce and Congress' to pass budgets, and the Fourteenth Amendments Debt Sovereignty Section, I have yet to see WTF the debt/deficit debate has to do with the Constitution, but it sure comes up a lot, without anyone remedying my ignorance.

That bothers me at least as much as the apparent conceit conservatives have a monopoly on the Constitution, though I admit that bothers me a lot, too. The Constitution is neither a liberal nor conservative document, but an American one. Liberals cherish many parts of the Constitution you neglected to mention; I was but one of many who sneered at Bushs "Free Speech Areas" on the grounds the First Amendment makes the whole nation a free speech area. In fact, the name particularly wrankled me because I used to live in Austin, too, and know darned good and well he lifted it from the area on UTs West Mall (a central part of campus, right in front of the iconic tower) reserved for decades specifically to provide student dissidents a prominent place to protest. Instead, Bush mockingly made it a means to justify moving any and all protesters at government events as far as possible from media coverage. In other words, he turned something intended to highlight dissent into a means of suppressing it.

I could go on reminding you of examples for a while (enemy combatants, the fact the IWR was not actually a declaration of war, etc. etc; for that matter, liberals complain about the war on drugs and gay marriage at least as much as Libertarians do) but you surely get my point. No one owns the US Constitution except Americans, a pretty large diverse group. Again, if some bunch of liberals started a FB "I <3 the Constitution" group and proceeded to use it to agitate exclusively against all conservative policies I would object just as strongly (for all I know there are dozens of such groups, but I have yet to encounter them.)

EDIT: I guess a lot of it boils down to your initial question:

The group did not present itself as anti-Obama, but pro-Constitution; it was only after joining I learned its founder(s) felt the two synonymous.