What exactly is the "terrible brexit deal"?
"Terrible brexit" will probably be more exact.
England will not have much say in European matters after
any brexit, i guess this should be understood?
So May wants to keep England /the UK (probably to soothe Ireland and Scotland, and keep England competitive) in the single market.
The latter is obvioulsly being seen as "treacherous" by the Brits?
It is also not seen as possible by the EU, since the initial and only reason for the existence of the EU is access to the single market by its
members without currency and customs problems, and a free ware and scientific exchange.
So you want to leave, but keep all advantages. Apart of a smell of cherry-picking this is most probably not possible. If the brexiters demand this they are delusional. If they say that May "wrecks" their brexit by trying to keep the UK having access to the single market they are just dumb.
I have some good advice for those big mouth brexiters: Do it yourself!