They are very different. A signing statement is, traditionally, a statement by the President that he considers some portion of a bill unconstitutional, and will act accordingly, e.g. not execute it. Constitutional scholars differ on this point, but there is a respectable argument that he is entitled to do this: the President is co-equal with the other two branches, and therefore entitled to interpret the constitutionality of his own actions just as they are.
There is a modern fetish for thinking that the Supreme Court alone interprets the Constitution, and therefore has the final word on what is, and is not, constitutional – but this is supported neither textually nor historically. The principle of Marbury v. Madison is merely that the Supreme Court is the ultimate arbiter of the constitutionality of Federal law. But there are many other actions of government other than law, e.g., in this case, the actions of the Executive. There is no text that supports the idea that the Supreme Court is superior to the President himself in interpreting the President’s own constitutional powers, and plenty of contrary historical precedent. I think the most intelligent observers conclude that each branch of government has equal right to decide the constitutionality of its own actions. Obviously, these decisions may come into conflict, and such conflicts are settled, when they are, extra-constitutionally, more or less by compromise under public pressure (cf. Gulf of Tonkin, sequelae of).
What the House is suing Obama over is something very different, and pretty much unprecedented. Obama did not look over the ACA and decide some portion of it was unconstitutional, and therefore not be executed. On the contrary, he agreed it was all constitutional, he just didn’t want it executed on the schedule set forth for it in the clear text of the law. That’s what all that “waiver” of the employer mandate, et cetera, was all about. He just took his pencil eraser and erased the “2014” where it was written into the statute and wrote “2015” instead. He doesn’t say the mandate isn’t constitutional, he just wants to implement the law in some other way than Congress wrote it. He is, in effect, rewriting the law to suit his own preferences.
That’s not allowed. The President executes the law but he cannot write it. That privilege lies with Congress alone. Admittedly, there are various ways of execution that have the effect of modifying the law, at least a little, in practice. But again, this is very different, and unprecedented, because the deadlines for the mandates were written down in black and white. They were specific dates. Obama just ignored them and set different dates. The ugly principle at work here is that if a President can alter the clear text of a law at his own discretion, then he can more or less rewrite law to suit him. Suppose the next President is Republican but faces a united Democratic Congress, and Congress passes a law, say, extending unemployment benefits to 150 weeks or something. Under the principle Obama has established (at least so far), our theoretical President R could just take out *his * eraser and change that 150 to 50 weeks, or even 5, at his whim. Or he could rub out the word “unemployment” and change the law to require 150 weeks of government support to every evangelical church, or 150 weeks of government wages to his favorite Aunt Hilda – whatever he wants.
I think if the Obama principle really did become established, and Presidents simply rewrote the text of laws to suit their preferences, this would be a dangerous development indeed. You are taking one giant step towards collapse of a separation of powers and towards tyranny, beause you are fusing executive and legislative power in one man. Add in the judicial, and you have Caesar.
But it’s not clear the principle will be established. Plenty of Presidents have tried to do outrageous and dangerous things, and if they lack sufficient support, they just kind of die out on their own. What the House is hoping to do is force this one to die a sharper, more notable death, so that it isn’t necessary to wait and see and hope it dies away naturally. I doubt it will work, though. You really can’t invoke the Judicial Branch to rein in the Executive, if you’re not willing or able to do so yourself. If Congress was serious about limiting the President’s power this way, they’d defund Obamacare until he executed its provisions faithfully. The House can do that: they control the purse. The fact that they don’t do this means they don’t have the balls. So, ultimately, while the objection and the legal theory are sound, this is sound and fury, signifying nothing.