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Fortunately you've allowed yourself some time to account for bad weather. A trip from coast to coast generally takes five days by the quickest routes. In your case, that would mean sticking to the Interstates for the bulk of the drive, so roughly I-8E to AZ-85N I-10E to I-17N to I-40E to I-44E to I-70E to I-76E to I-81N to I-78E.

The chances of getting absolutely stuck on the Interstate are rather slim since they tend to be well cared for in the Winter months, especially in the Eastern states since the traffic volume is significantly heavier than the Rocky Mountain states.