I watch the GPS market fairly closely, and I don't think there are any units designed for in-car use that do this. If someone knows different, speak up.
Units designed for aviation and marine use will do this. Unfortunately it's the lower end units in these markets that are considered portable, the higher end units are OEM and panel mount, and in general the live weather radar is only in the higher end units. The graphics are enormously better in the high end units compared to the 4,5 and 6" screens in automobile units.
Your alternative might be a smart phone with some good GPS software loaded, and use the web interface for the weather radar. AccuWeather has what I'd call near real time weather radar, as does intellicast. Neither charge for access to this.
Edit: You got me looking around. The Garmin
GPSMAP 376C might work, it uses XM Satellite Weather, but it stretches the meaning of portable, and it's not cheap, MSRP $900. I think you can spend less and get a good in car unit and a smartphone with internet access.