Pushy broad = an arrogant obnoxious power hungry woman - often quite douchey in her manner. Many pushy broads live for their careers and will do whatever-it-takes to get ahead in the corporate world. Manners and tact are foreign to most of these women - as the ticket to the top is often sought & acheived by being arrogant, pushy and obnoxious. Most of these broads are cold as ice, often possessing no sense of humility or humor. Being a classy lady is usually not a characteristic trait for these kind of women.
Many of these pushy broads could also be defined as doucheys - douche bags. Women with balls !
One of my former managers was a pushy broad - Whoa, she could, and would, cut your balls off in an instant. She could, and often did, push her way into any business situation - the bottom line, she acheived her goals, but she had no class.