I don't think so. Not for 4 months.
I've spent extensive time hiking across the US, 14,000 miles over the course of years. That's about as cheap as you can get, sleeping mostly in the woods, eating ramen most nights.
And even then a hiker budget is 1k-1.5k/month, for one person.
Considering you'll have the added expense of vehicle, gas, paying $20-30/night camping fees, and then hotels ontop of that. Just food alone in the US it's hard to get under $20/day per person anymore, and that's with minimal restaurant meals.
I think this budget would be doable for 2 months, but 4 is really pushing it.
Happens a lot. In the airport we saw a guy being denied boarding at the gate for a flight to Vietnam, we assume because he didn't have a visa.
We made that assumption and was paying attention to that flight because we were also supposed to be on that flight, but decided to double check visa requirements the night before and found out lol. So instead we were taking a flight to KL that was leaving at the same gate an hour later.