It is nearly impossible to give an easy and short answer to this.
A blue card is valid 3 Month after the job has ended, but in the first 2 years you need yo ask for permission if you want to change your job with a blue card
A quick research shows me that there are several types of visa but more important is, that your possibilities depend on your qualification, your financial situation, your nationality and also on your knowledge of the German language.
Sometimes it can be a problem, if you entered the country on a working visa basis and later you want to change it to a permanent status, as far as I understand the law. But I'm not an expert ...
You should seek assistance from an organisation like Caritas, IHK, sometimes at Universities or if you can afford it, contact a lawyer who is specialized in "Ausländerrecht"
After reading this http://www.bamf.de/EN/Infothek/FragenAntworten/BlaueKarteEU/blaue-karte-eu-node.html
What are the permit implications of voluntarily leaving a job as a US citizen Blue Card-holder in Germany?
(read his answer) I guess it can be an advantage not to have received the BC yet.
If you find a better job soon, it's maybe better to apply for a BC with the new job