If you have a U.S. bachelors degree (or the foreign equivalent) you qualify for an H-1B visa provided that you will be working in a field that requires a degree and the degree required is related to the type of degree that you have. If you do not have your master's by April 1, 2014, you will not get two chances at the H-1 lottery since there is a separate lottery for U.S. Master's degree holders.
Also, be careful with any potential employers that you are not misrepresenting yourself as someone with a Master's degree if you will not actually have one by December 2013. If a company finds out, they could terminate you and the H-1 would be automatically revoked so disclose the information up front.
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You should speak with a lawyer in depth. However, it does not sound like there should be problems. If you switch to the H, you would have to enter and exit to have your passport stamped, but as long as you are in valid F status, you can make the H application in the US.