When any politician says something is a "threat to democracy", they are feeding a soundbite to the media in the hope it will be repeated and become an accepted truth.
The only real threat to democracy is the fostering of public ignorance, e.g. false choices like "my deal or no deal", turning the public against parliament with populist rhetoric, etc...
May has worked tirelessly to re-define what the referendum result means, under the smokescreen of "Brexit mean Brexit" and "the will of the people". Political tribalism and right-wing media enable that process.
Parliament's job is not to enable a minority extremist agenda. If the PM won't change course, the only sensible thing they CAN do is to stop the clock by revoking Article 50.
Private instance for me & my bots