> would it be OK if I tell the HR manager that I would provide her with
> another reference, for instance saying that my supervisors are not
> happy that I am looking for a job when I have to concentrate on
> preparing my defense (sounds like a lame excuse but I can't come up
> with something more plausible), or is it not a good idea at all?

It was a huge mistake for you not to check in with your references before you used their names.

First, you want to get their permission to be references. Second, you want to ensure that they will say nice things about you.

At this stage, you shouldn't make up any excuse or say that your supervisors are not happy without knowing the facts. Instead, call your references and ask if they would please respond to this HR manager. Then tell the HR manager that you have contacted your references.

> Moreover, what if my supervisors don't respond at all? What would the
> company do? Would they ask me for new reference or they flat out go on
> with their next candidate?

While you never know for sure, most reference-checkers would ask for new references. When I checked references, I always wanted three. If I couldn't get in contact with three, I'd inform the candidate.