If you really have a "contract", and not just an employee handbook upon which you're basing your arguments then "no", an employer may not do this. A contract is a document containing mutually binding obligations Your employer obliged itself to pay you on the 20th of each month, not the 30th. Is this a material breach to you? Meaning, does it financially impact you in a negative way? You are receiving the same compensation, I presume. Albeit, at a later time.
As to your rights to a severance, it may be conditioned upon the employer discharging you without cause. Be careful before you ask for a termination because a resignation may disqualify you from a severance package. At least, most well-written employment contracts disqualify resignation from severance.
Consult a lawyer in your jurisdiction to interpet your contract.