It is quite difficult, inasmuch as your authorized stay on the visitor's visa is at most 6 months.
Now, if a company will sponsor you for the H-1B, the application process will only begin on April 1, 2013, and your work cannot start until October 1, 2013. Therefore, to remain in the US in a legal status, you cannot change status from B2 to H-1B directly. To evaluate your options, you must consult with an experienced immigration attorney.
Contact attorney Gintare Grigaite, Esq. at 201-471-7989, located in New York and New Jersey. Answers on AVVO do not constitute legal advice and do not form attorney-client relationship. Always consult an attorney for a legal advice.
You need an attorney. You must file for a change of status prior to the expiration of your current status and be sure to meet all the requirements of the proposed status.
Whether or not you can change your status also depends on whether or not you entered the United States on the Visa Waiver Program.
The materials provide here are given for informational use only, and are in no way intended to constitute legal advice or the opinions of this law firm or any of its attorneys.
This is a very complicated matter, and you should seek the help of an attorney.
Your employer will need to file for an H-1B at the beginning of April 2013. You will then have to apply for an H-1B visa stamp in late September 2013, and would then enter the US no earlier than September 20, 2013 with that visa stamp.