What is the minimum time frame needed for regression testing before go-live

Seriously. We (as in test/quality/ whatever we are called where you work) do not define timelines. We do tell "The Business" what we can do with the time allocated, how much time we think we need to do the job properly, and what the risks of cutting corners are. But whether to accept that level of risk is a business decision and not a quality one. When asked to do testing such as you are it is imperative that you get actual sign off from your superiors and preferably from the customer (whoever that is in your environment) that the level of risk involved is acceptable and this means you need to give them a proper assessment of that risk. It does not mean presenting a doom and gloom scenario that everything will fail because it has not been "fully" tested (of course nothing is ever fully tested), it means honestly and clearly assessing how risky each change is to introduce defects in other areas of the code, what is the worst that could happen, what is likely to happen, and how likely is each to happen. Once you have provided that assessment and gotten signoff that the level of risk is acceptable then you have done your job and no one can fault you if serious defects are introduced into the production environment.