There's a lot of discussion in here about how many cars would get taken off. That's not how HSR works.
There's two kinds of travelers:
1) Time sensitive. These are the people who are flying today. And half the time these people aren't even paying their own fare. Work is usually paying. What matters to this group is door-to-door travel times when you include transit time to the airport, pre-boarding time, transit time from the airport, etc. This group may even consider same day roundtrips for a meeting. Most HSR systems elsewhere have grabbed huge marketshare with these groups. In some countries, enough to hurt the national career. See Italy as an example.
2) Fare sensitive. This is the group that drives. They are looking at total cost. And that calculation even looks at the cost of a rental on the other side. Highly unlikely this group will take HSR. They won't even take a train or bus now. Most people in this group will only ever look at the cost of gas. Cost of the car, insurance, consumables like tires, etc are sunk costs.
In places with HSR systems what you'll see is fluidity between the two groups. The exec who takes HSR for his weekly meeting in a city 300 km away, will still drive the family to the cottage in a van on the weekend. Meanwhile, some fare sensitive can get picked up occasionally when they realize they can do an out and back trip without staying in a hotel. And a lot of companies who do pay mileage will start choosing to simply buy rail passes if they can avoid overnight hotels or get extra productivity out of that employee. Do you really want an employee who makes $50/hr wasting 6 hrs on a trip between Calgary and Edmonton?