And especially now: How do you refuse something to David Cameron's UK (a big member state), but hand it to Switzerland (a small non-member state)?
In the case of the UK, it would demolish the very core idea and foundation of the EU. This UK parallel makes it very, very unlikely that the EU would give anything to Switzerland that could even only hint at flexibility in this matter.
The "best" outcome Switzerland can hope for (unless they repeal that immigration reform) is a state where Switzerland is in breach of the treaties, but the EU looks the other way, either on purpose, or because the member states cannot agree on a way to handle the situation. This couldn't last forever, though.
And by the way: Trying to have a treaty re-negotiated has already worked out not so very well for Switzerland in the case of Zurich airport. ;-)
Although I have to admit, we Germans basically did the same thing to Switzerland in the case of the CDs with tax data. It is a shitty thing to do.