Considering those poll number I linked to, they might just decide that the best way to uphold the constitution, in your hypothetical scenario, is by putting Trump in office.

Re: "I don't think anti-war qualifies as anti-military.", I rather doubt the actual service members themselves see liberals that way. Being anti-war, of necessity, comes with views that prevent the military from doing its job, whether it be budget cuts or political restraints that risk lives or interfere with legitimate military goals during ongoing operations.