My Teabagger friend gave this response to the late night GOP House Rule change...

[JHB]

22. Ok, technically they have the right to do it. By that standard...

...any president also has the right, in his capacity of commander-in-chief under Article II, section 2, paragraph 1, to surround the Capitol with artillery and file one or two shots onto its surrounding grounds just to get the range.

Just because a president technically could doesn't mean it's anything close to a good idea. Neither is what the House Republicans are doing.

Edited to add: Considering his likely response: Under my hypothetical presidential scenario, sure, the troops would likely balk at what he was doing. That's what we are doing. He's the one arguing that the hypothetical president has every right to decide where the guns are pointed.