The analogy is not exact. Try imposing a constitutional change (not an interpretation, a real written change) in the US Constitution in the same sleazy way.
Yes, the US government would love to be able to do something like that. That's why they use wartime or emergency conditions to "bend the rules"; when the public is united against a foreign menace, and much less likely to oppose it. In peacetime there would have been all kinds of legal challenges.
In the case of the EU they are trying to impose the whole document, all 300 or 400 pages of it!
It does not need that the "right to bear arms" is written into a constitution ("treaty") since it is, ultimately, an inalienable right. Indeed, in some new member states, they must be awash with AK47s and, with studied indifference to the wants of the British people, Tony has allowed vast numbers to enter the UK from these states (with or without AK47s) which is something other older member states were careful not to do, though Tony probably didn't wonder why this was. It might perhaps be that other members prefer the predictability of their indigenous populations rather than the uncertainties of a "Salad bowl".
We may be surprised the French allowed a referendum last time around but please note how well this current behaviour conforms to the practise described by me in a previous post when describing the French approach to passing unpopular laws:
Government announce unpopular measure.
Citizens dig up the streets.
Gendarmes stand around and watch to make sure no foreigner does anything silly e.g. British Lorry drivers.
If the population gives up and goes home, all is well.
If not then the Government recants, they go home, the streets are repaired, they wait a while and then presents it anew in slightly disguised format and push it through without much further ado.
In this instance, however, should we consider a referendum a suitable substitute for digging the streets or will the citizenry still insist on observing the established procedures?
What behaviour we might expect of the newly joined members is uncertain since they may not yet be aware they have exchanged one totalitarian regime for another and may still believe the EU to be a democratic Union where the population's wants are treated with some regard. Their new overlords have not yet substituted their own control over the new members to replace that exercised by their former overlords.
Could be interesting and reminds me that at least one American study of the EU suggested that it could all end in bloodshed and tears.