Are there any severe side effects with taking celebrex (celecoxib) for 2 weeks with coumadin?

Not the best idea. As dr. Rosenfeld said, taking both together can certainly increase your risk of bleeding. It is possible to take an anti-inflammatory medicine while on Coumadin but you are probably better off not. If you do take it, you will also need to check you INR to make sure the Celebrex (celecoxib) isn't affecting the effectveness of the coumadin.
Avoid. The combination may increase the risk of gastointestinal bleeding.