It would be a blow, but the Romulan Empire would keep chugging along. Romulus might have been the home planet, but the empire was huge. I did a quick Google image search for trek maps, and while they're all a bit different, the Romulan Empire was comparable in size to the Klingon Empire and the Cardassian Union.
I don't see why the Empire would erode at all or face additional threats from its neighbors. Their battle ships would still be out there patrolling and any ships stationed on Romulus would have taken off, in tact, with refugees. They had some warning, so the leaders would have set up a base of operations elsewhere. There's no indication that all their shipyards and manufacturing were concentrated on Romulus. And the fact that the Narda existed means that mining took place on other planets.
If Washington D.C. were to be nuked a couple weeks from now, it's not like states would secede and Mexico would invade. We'd definitely lose something, but the infrastructure and the military are still there. Farming and manufacturing would go on, local and state governments would be fine, the federal agencies would reform themselves quickly enough.