Travelling to US for first time within one month of visa expiry h1b

[Nonim]

Hi
My visa was issued on Jun 26 2012.
Petition date/h1 b expiry date - Mar 9
My employer has booked my tickets for Feb 1

So I just have about a month time to file for extension and as it is feb I just have a mere 27 days left in the clock. As I am travelling for the first time I don't have a SSN as well

What are my chances of filing the extension realistically?
Will I be questioned at POE about late travel though I was issued only for 9 months at the first place
Is there any chance that the immigration officer will issue me I94 form for more days than actual expiry
What are your suggestions?

Any response is much appreciated