Can I travel coast to coast in USA on one highway or would i gave to change highways?

The closest you'll get is I-10.  It gets pretty close to the Atlantic in Jacksonville and almost to the Pacific in LA.  

I-80 comes fairly close to the Atlantic, hitting I-95 just outside of NYC.  It's other end is in San Francisco (it crosses over the bay, which is an extension of the Pacific).

I-90 runs from Boston Harbor to I-5 in Seattle.  

You might be able to do it on a couple of US highways, although none of those are truely a straight route.  

yes.  I-10 runs from Los Angeles to Jacksonville FLA.

I-10 LA California to Jacksonville FL. (watch out for Florida Man) is about as coast to coast as one can get. But as the answer "?" said, how CLOSE I-10 officially starts AT the "coast" and ends at the other is debatable. Maybe I 10 has a boat ramp at each end!!

Now, here l am not trying to be funny. I-10 seems to end just before Brooklyn in Jacksonville. It looks like 20 to 22 miles from the coast. Brooklyn, yeah...

Daniel chimed in with another great answer and explanation.

We have interstates that run generally east/west (not straight lines by any means).  The two that I can think of are I-80 and I-10.  Exactly how close they get you to the actual shore, I don’t know.  

there are several ways to travel coast to coast on one highway