Can I stay in US untl H1 B petition is decided?

I am on J1 visa that expires on December 31st 2016. My H1 B (I-129) is filed on September 8th. Should I go back to India before 31st December) and come back? Can I continue to stay in the US even after 31st December? Will there be a problem if I travel and return when H1 B is approved.