Hi there,
Now, now... Let's not be too hasty on blaming your "local" HR reps about the delay in your iqama. There are new regulations in the Kingdom, and there are many engineers experiencing some degree of inconvenience related to the new regulation.
Now, the new regulation requires that prior to the issuance of your iqama - since your work visa indicates you are an engineer - you need to apply first for your membership in Saudi Council, which is the equivalent to your home country licensing body. Only when your Saudi Council (license) Card is issued can you proceed to the application for your iqama.
The Saudi Council registration may take time. There are many factors involved, all causing the extended amount of time needed to issue your Saudi council, which are as follow:
1. The software system (program) is new. There could be some glitches.
2. The first step in the Saudi Council membership is the VERIFICATION of your records, whether the certificates and your CV you submitted online are true and correct. This process can last up to a month, depending on how quick they can get hold of your school or your previous companies to verify the details on your certificates.
Oh by the way, you need to pay first the verification process before it can actually begin. Since you don't have an iqama, arrange with your company to pay the bill online using their credit card. When the payment is received online, you will receive a notification via sms and email that the payment has been received and that the verification process has started. It may take up to a month.
3. Only after the verification process can you proceed with the registration per se.
4. Once the registration is done, your credentials (as far as I know) will be linked to the Saudi Ministry of Labor to issue your iqama. This part here is what I'm not sure of the process.
So given your scenario, I doubt you are to get your iqama any time soon without your Saudi Council (license) card.
What can happen?
As long as you were able to comply with the requirements of Saudi Council, you and your company should be off the hook legally speaking. Just make sure to receive your salary in cash, as you are unlikely to be allowed to make any bank transactions. Hospitals are likely to deny you any health care services unless it is an emergency.