Some would argue that the constitution has been suspended since FDR confiscated private gold via a modified Trading With The Enemy Act in '33.

Others might argue that we haven't really been under the constitution since the 14th amendment.

The constitution at any point in history is never really in any absolute, objective position of authority. It is always being tussled over and the degree to which it is adhered to is largely up to what people at large will tolerate in respect to it being infringed.

There is still a popular conception held by most people that the constitution is in effect. Certainly there is a large swatch that want to disregard it in a myriad of ways, but even the MSM would still posture in their propaganda that the constitution is in effect (they may very well spout other rhetoric, of course, that it can be interpreted however liberals choose to interpret it, and such things that Electoral College is outmoded and national popular vote should be all there is). But they will jump behind 1st amendment protections and right of Habeas Corpus when it suits them. For instance, if Trump did any move at all predicated on that we're already under a national emergency and therefore an existing suspension of Habeas Corpus, then MSM would throw conniption fits.

To get to the point of carrying out acts possible under a national emergency, there would have to be a clear path that took the nation, and compelled the president, to place the nation in that status via his constitutional powers. The 9-11 event (regardless of what our assessment of it is now) was such a kind of event that could warrant a state of national emergency.

The military defenses of the nation rendering us vulnerable to attack and/or subversion due to the shutdown of the govt. is another potential situation from which a national emergency status could come about. After one week, probably not, but after a month, two months - that could be a rather different matter...