Timeframe for entering the U.S. prior to H4 expiry date???? Advice needed

[Quest55]

Hi all,

My info is as under:

Currently in India on H4 and working.

H4 expires Sept 3, 2011.

AOS-I485 pending.

Given the state of H4 renewals at present, my question for seeking advice:

How many days prior to the expiry of the H4 visa am I allowed entry into the U.S. or will I be allowed entry upto the last day i.e. Sept 3?