I wouldn't give it a second thought. If you are worried, get a NOAA weather radio and kep it on. The NWS does a great job of getting the warnings and advisories out.
Several million people are LIVING there full time and the vast majority of them do just fine. Ever have a storm where YOU live? Would you travel THERE?
We've been stationed in Oklahoma for 6 out of the last 12 years. We were there and IN the May 3rd 99 tornado that hit OKC. Just get a battery powered NOAA radio like aksnowman said, and keep it on. Also, along the interstates will be signs that say, "for local weather conditions, tune to XXXXX station" If something bad is happening, you will know about it, because that will be ALL the radio talks about, they completely abort normal broadcasting. A CB is also handy, because the truckers will be talking about where to go (overpasses, gas stations, etc.) to seek cover if it gets that bad.