Griff got in ahead of me -- I went off to make the scene of the
Deathly Hallows midnight-plus-one -- hey, as I type we just looked under the front doormat and there's our copy; UPS must not be ringing doorbells today to speed their operation, so there's
in our house -- but yeah, Article I Section 8-11. Section 8 enumerates the Constitutional powers of Congress. It does NOT state that Congress has the sole power to call out the troops; indeed it doesn't seem to give it such power at all. Calling up the troops really seems much more directly related to the Commander In Chief anyway.
America has been in about a hundred and fifty shootin' conflicts, and if gunfire is quacks, well, they'll certainly do. Only five of these were Congressionally declared. Undeclared conflicts started almost immediately with an undeclared naval war with France -- the Quasi-War with France, 1797-1800, over treaty provisions that had come into what must have been regarded as very unfortunate conflict. After a couple of years, negotiation and claims adjustment, basically, settled things. Some of them -- a few claims continued unsettled into the twentieth century. I'm quite surprised to read
here in the National Archives' Prologue Magazine that this ruckus led directly to the Louisiana Purchase as an integral part of trying to get matters settled.