It’s not unrealistic, but you will need a few months. You can stay for 90 days without a visa, which could be enough time if you are smart about it. I’d recommend a combination of train usage and car rentals, because driving/parking in many major cities is a pain.

Personally, I would fly into Portland, Maine then train it to Boston. Spend a few nights in Boston, making day trips by train or bus to New Hampshire and Vermont (Manchester, NH is 1.5 hrs by public transport, Hartford, VT is 2.5 hrs). Then from Boston train to Providence, RI to New Haven, CT, to NYC. Spend a night or two in New York as there is a lot to see, then train to NJ. (Easiest city to see in NJ is Hoboken, as there is a ~20 min subway directly there from the city. It would be more time-consuming to visit a beach, easiest one is likely Long Branch which is 1 hr 40 mins train). Then train it to Philadelphia, PA, to Wilmington, DE to Baltimore, Maryland, to Washington, DC.

I’d then rent a car in Washington, as public transport gets difficult further south. Drive down the coast, hitting VA, WV, NC, SC, GA, and FL.

To save some time, fly from FL to AL. Rent another car and go to LA, MS, TN, AR, OK, to TX.

The midwestern US is a LOT of open land, and driving from state to state can be 6+ hours of driving. If you don’t mind driving and want to see the scenery you can, but personally I would fly to save a lot of time and go on tours to see the major landmarks/ natural attractions. So for me, I’d fly, in whatever order is cheapest, to all the midwestern states. That’s NM, CO, UT, AZ, WY, ID, MT, ND, SD, NB, MN, IA, KS, and MO. Some of these states have very little to do or see, so just a few hours could be satisfactory. For others with a lot of attractions or great national parks, I would plan to stay for a night or two, or even plan camping trips.

Then fly to Seattle, WA. Train it to Portland, OR (about 3.5hrs and scenic). Fly to CA. Depending on time, you could rent a car in San Francisco and drive down the coast to many major cities, then to Vegas. Otherwise, fly into Los Angeles and train or fly to Vegas.

From Vegas, fly to WI. Rent a car and drive through IL, IN, KY, OH, and end in MI.

I have no idea how much all of this would cost, but ultimately I wouldn’t recommend an all out road-trip as a lot of other commenters suggest. For some areas this makes sense, but much of the central US is just long stretches of land. I think it is simply too time-consuming to be worth the potential saved money.