That would cover the military and agencies such as EPA, FDA, USDA, and CDC that work to ensure security and safe food and water. It is hard to argue that the government taking over an entire business sector falls into the category of "general welfare."
Far too often, people misinterpret the general welfare clause as meaning that the government should provide permanent dole, or that the government should be everyone's sugar daddy.
Sorry, but it states CONGRESS shall, NOT Department XYZ. There is nothing from We the People that allows Congress to abdicate their powers nor responsibilities that We have bestowed upon them.
Regardless, one clause (general welfare) would NOT (can not) supersede the whole of the Constitution as laid out.
In the 1819 case M'Culloch v. Maryland, Chief Justice Marshall said in his opinion ... "Let the end be legitimate, let it be within the scope of the Constitution, and all means which are appropriate, which are plainly adapted to that end, which are not prohibited, but consistent with the letter and spirit of the Constitution, are constitutional."
Please note: I am not for Obamacare, but it was passed by Congress and signed into law by Obama. So we are - temporarlly - stuck with a lousy law.