Birth Ceritificate date of birth discrepancy

My wife was able to get her birth certificate in English from India but the date of birth in that does not match with the date of birth in all her other documents including Passport (just off by 3 days). Here are my questions:

  1. Is it a big deal for the GC processing (I-485)?
  2. If it is, what can be done to rectify in India or USA? (The local municipality in India denied to correct the birth certificate, they want us to update the DOB in all other documents)

It is usually a big deal.
You should ideally correct the birth date on all other documents to match the birth certificate.

Is it sufficient to correct it just in the passport for GC processing or get that started?