A person's privilege to drive on public roads should be contingent only upon their ability to use those roads safely and without excessive risk to others — for example, by demonstrating driving competency through a test and by having insurance and a safe driving history.
The motivation to deny driving privileges to illegal immigrants is to make it more difficult for them to live here. It's an incentive for them to leave.
If we accept the principle of denying driving privileges to certain lawbreakers, how far could we take it? We could make life less comfortable for all manner of scoundrels! We should surely start with convicted felons. Petty thieves, too — they can find somewhere else to live! We could also go after deadbeat dads who are behind on their child support payments. We don't want those kinds of people living in Oregon, right? If they can't drive here, they'll leave!
But that is obviously illegitimate. The purpose of government is to protect individual rights — not to make everyday life as difficult as possible for people that "society" doesn't like!
Driving privileges should not be encumbered by unrelated goals like the enforcement of immigration laws.
Certainly, there are flaws in this bill. The key problem is that it creates an obviously different type of identification than a regular driver license, creating the risk that people using a driver card may be subject to additional suspicion, harassment, or other hardship based on the reasonable assumption that they are violating immigration laws. Importantly, the state's database of driver card holders would be valuable data for federal immigration law enforcement, who might seize it.
It would have been much better to have a single form of driver identification for everyone.
On the whole, however, I believe the benefits of this bill outweigh its problems. Driving privileges should not be coupled with immigration status. These are separate concerns that should be treated separately by the law.