If any U.S. president or other official declared he was suspending the Constitution, he would be immediately arrested.

The presidential swears (or affirms) in his oath of office to "preserve, protect, and defend the Constitution of the United States."

Other federal officials have similar responsibilities.

If such a president were backed by a dictatorial party that somehow controlled Congress and the Supreme Court as well (unlikely, but hey), and these branches concurred in suspending the Constitution, and arrests were impracticable, the despots would have to answer to the U.S. military, whose members are pledged to "support and defend the Constitution."

If there were serious disagreement within the military, of course, the result would be civil war.   

But now we're talking about bizarre sci-fi possibilities in an Orwellian future, not the actuality of ten thousand gun homicides a year, right now.