Yes there is always a chance of bad weather along any route from the west to east or east to west. The interstates are pretty safe even in bad weather and as long as you pay attention to the severe weather broadcasts so you can avoid possible problem areas.
Tornado and heavy rain storms are usually short lived so if there is a warning for the area you will be traveling stop somewhere safe and wait it out if you can't get ahead of the storm.
Most large cities have circular routes around the city so you can avoid going through the main part of the city. For example El Paso HWY 375 bypasses the city and gets you back to I-10 east of the city. However if you hit the city at the right time of day or day of the week when traffic is less then straight through works. Avoid normal commute times and you will be OK.