There are MPs who genuinely think David Davis could somehow force the EU into accepting a deal. What is remarkable about these negotiations is that 27 governments have been largely united on one side, more or less speaking as one: and a single government on the other side has been riven by division, the reason being of course that the UK is split down the middle on this: and the people charged with doing "Brexit" are reluctant leavers, but the keener leavers have preferred to leave things to the former and merely carp from the sidelines, A state of affairs that leaves the PM in a pretty impossible position.
In any case, as I said earlier, "no deal" does not necessarily mean we would leave: it's not necessarily the default option many seem to think: for a start it would very likely not get through parliament and there might well have to be a referendum or even a general election. Ironically it's this fact that probably gives May some leverage with the fanatics. As for leverage with the EU, I am still putting my money on a deal, but not as much as I was prepared to earlier.