How many people? My wife and I travel on the Empire Builder in coach. The bedrooms and Roomettes can be pricey if you have 3 or 4 in your party.
There are usually 3 to 4 times as many people sleeping in coach than are in the sleeper cars.
Take the Empire Builder to Whitefish MT and rent the car there to go see Glacier NP including the Going to the Sun Road. You should stay at least 1 night on the east side of the park before heading back to Whitefish.
If you feel the need to spend a night in a sleeper car, try it from Whitefish to Portland or Seattle. Skip Mt. Rushmore for another trip including Devils Tower and Yellowstone by car.
Rent another car in Portland for your trip over to Bend.
There are many great places to stay in Bend. Our closest airport is in Redmond about 15 miles north of Bend (RDM).
The other way to use Amtrak from Bend is to take the Amtrak Shuttle bus from Bend to Chemult and take the Coast Starlight north to Portland (morning) or south to Sacramento (overnight).
Would you believe - Bend has a new brewery under construction!
It's on the east side on US 20 just east of 27th St (Worthy).

Thank you so much for responding so quickly, but we have totally ruled out train. Even coach is out of the budget we want to budget for expense on the trip. Also want to focus on seeing as much of the Northwest including Rushmore because we are dividing our long trips into quadrants to reach our ultimate goal of seeing all 50 states... then branching out to the UK!!

Check and see if you can drop your rental car without a big fee in Reno/Tahoe. That airport is a SW hub.
Leaving IL you will go through IA, MN, SD, ND, MT (Glacier), ID, WA, Oregon (Bend), CA and up I-80 from Sacramento to Reno.
With a little more time you could drive across the Great Basin to Salt Lake City and across southern Wyoming to Cheyenne and south to Denver to add 3 more states.
While you are in the Rapid City/Mt. Rushmore area you could go over to Devil's Tower to catch the NE corner of WY.
Go north on US 85 past the geographic center of the US to get into ND and I-90. Take I-90 all the way to Butte and then north on I-15 to Shelby to get on US 2 into Glacier.
Did you have your heart set on Seattle or Portland or will you just head south from Spokane and cross the Columbia at Biggs on US 97 to come south to Bend?
The best hotel in Spokane is the Davenport IMO.
Anyone else have a better plan?
Also did you see the 15, 30 and 45 day USA Rail Passes while you were shopping on the Amtrak site? It's hidden under Deals.

They said no train, Tom.

Amtrak should pay the guy(!) He finds a way for every itinerary to include trains . . . and dropping a car in NV to save $$

"Expect trip duration to be about 2 to 3 weeks. "

Really depends on if you mean 2 weeks or 3 weeks. The Redwoods and Northern CA are terrific but I would not consider going that far south unless you can swing 3 weeks. There is so much to see/do in Glacier/WA/OR that you can easily fill 2 weeks.

But w/ 3 weeks you could squeeze in Redwood National Park and then Lassen/Burney Falls/Mt Shasta. You could then drive back north and fly out of Portland or south and fly out of Sacramento.

As for accommodations - What is your budget

During your stay in Glacier National Park, spend the majority of your time on the east side, preferably the Many Glacier area. The Many Glacier Lodge sits on Swiftcurrent Lake and the views are spectacular. There's also Swiftcurrent Motor Inn closeby. That's a popular time of year and reservations in the park will be difficult to get, however. If you can't get either one of those, try St. Mary Lodge in St. Mary- also a park property. Outside of the park, try Pinnacle Cottages or Glacier Trailhead Cabins.

The Going to the Sun Road connectes the east and west side of the park and is one of the most scenic drives in the country. I would make the entire drive across and then on your last night or two, spend the night on the west side of the park. Lake McDonald Lodge is inside the park, but on the west side there's tons of lodging just outside the park in West Glacier, Columbia Falls and Whitefish.

The best hiking is on the east side as well. Two of the most popular hikes are to Iceberg Lake and Grinnell Glacier. If you decide to hike to Grinnell Glacier and want the shorter hike via the boat, be sure to make your reservations a day or two in advance as the boat fills up quickly.

http://www.hikinginglacier.com/iceberg-lake.htm

http://www.hikinginglacier.com/grinnell-glacier.htm

Off the Going to the Sun Road, be sure to stop at Logan Pass Visitor's Center (but get there by 10AM or the parking lot will be full) and take the hike up to Hidden Lake Overlook where you're almost always guaranteed to see mountain goats. Also, check out Virginia Falls/St. Mary Falls - both short hikes as well.

http://www.hikinginglacier.com/hidden-lake-overlook.htm

There will be construction on the GTTS road so expect delays, but enjoy the spectacular views while you wait!!

<<Take I-90 all the way to Butte and then north on I-15 to Shelby to get on US 2 into Glacier.>>

This would require some backtracking.

Once you get into MT, you will have several options for getting to Glacier. If you're coming from ND, then you could take highway 12 and 200 from Billings to Great Falls and then go North on Interstate 15 until you hit hwy 200 which will bring you to East Glacier; this is going to be the most direct route for you.

Or you can stay on I-90 past Billings and then head North on hwy 191 and go through Great Falls. YOu could also stay on I-90 to Missoula and then head North on hwy 93.

There are many great microbrews in MT. My favorite places to stay in MT include the Many Glaciers area of Glacier Nat'l Park, Whitefish, and Missoula.

I agree that the Davenport is a nice hotel in Spokane. Also, check out the Hotel Lusso which is across the street from the Davenport.

Montana is long and boring no matter whether you drive the Interstates or the US routes.
Here is my stab at your route: Springfield to Luverne MN (via Mason City) 9 hours. Luverne to Mitchell SD lunch and see the Corn Palace. Mitchell to Mr. Rushmore 4.5 hours 300 mi.
Spend time in western SD and see Devils tower. Spend a night in Miles City MT-see the Range Riders Museum. Miles City to Browning, MT-see the Museum of the Plains Indian 7 hours 460 mi.
From Browning go through St. Mary and up over the GTTS road. Decide how long you are spending in the Glacier NP area. Spend a night in Whitefish. Whitefish to Spokane via Couer 'd Alene (sic) is 4.5 hours 250 miles. Spokane to Bend is 6.5 hours (via Biggs) 386 miles. Bend to Crescent City CA via US 199 and Redwood NP is 5.5 hours. Crescent City to Sacramento is 7 hours 375 miles. Sacramento to Reno is only 2.5 hours 135 miles. You can drive the rental car all the way back to Springfield in 4 long days with stops in Salt Lake City UT, Cheyenne, WY and York, Nebraska. Driving all the way with enough time to enjoy what you want to see this route would take about 20 days.
As for Amtrak, I'm driving to Yuma AZ starting Friday morning instead of taking the train by way of Los Angeles.
If I had driven every place I rode Amtrak to in the last 10 years, my 2003 Civic would have a lot more than the 219K that it has now. Cost per mile is comparable for a single driver. The car with a couple of passengers will always be cheaper than Amtrak.

<<Montana is long and boring no matter whether you drive the Interstates or the US routes.>>

It's a big state, but I sure wouldn't say it's boring.

Eastern Washington for wine - particularly Walla Walla
Olympic National Park - massive temperate rain forests, craggy alpine country, wildernesses beaches, one of the deepest natural lakes in the world
San Juan Islands and Victoria B.C. laid back boating with ample wildlife, Victoria's British flavor and the stunning Buchart Gardens
Mt. Rainier & Mt. St. Helens - volcano country in a way no other mainland area can do volcano country
North Cascades National Park - outstanding drive through rugged mountains often shown as a lead-in for a film company (Paramount?)
Columbia Gorge - drive historic national scenic byway through the greatest concentration of waterfalls in the US along the massive Columbia splitting the Cascades in half (very dramatic)
Oregon's Willamette Valley - wine, cheese, antiques, verdant valley
Oregon Coast - greatest stretch of publicly-owned beaches in the country (300 miles)

A route might go over the N. Cascades Highway to the San Juans and on to Victoria. Then ferry back to the Olympic Peninsula for 3 - 5 days circling to the south, then east past Mt. St. Helens and then northeast up and over Mt. Rainier,into wine country and Walla Walla. Then head west again through the Columbia Gorge through Portland and on to the Oregon coast. Turn south along the northern coast, then head back across the Coastal Range into the Willamette Valley. Head down to Ashland for America's best Shakespeare and theater town. From there, head back through the southern Cascades over and around Crater Lake. Continue north through the Cascades to Bend. Two weeks for that, and a lifetime of memories.

I can always get more specific with you if you'd like. Oh, and did I mention how great Seattle, Portland, and Vancouver are?

Drew Bledsoe's hometown was Walla Walla and his vineyard is there. http://fruitgrowersnews.com/index.php/magazine/article/drew-bledsoe-scores-touchdown-with-winery
When he retired from football, he built a very nice home in Bend Oregon.
If you like wine, try Doubleback.