I'm sorry but EPA not having enough money is bullshit. They "only" have enough money to test 20% of new cars, therefore Volkswagon was able to cheat, so give us more money?
IRS tests (audits) less than one percent of income tax returns. Yet tax compliance is quite high in the United States, relatively to other countries. Why is that? Because IRS has teeth and people know if you get caught flagrantly cheating on your taxes, they can seize your bank accounts and your house and put you in jail.
Testing 20% is more than enough, you just gotta give EPA some teeth. Start by putting VW CEO in jail and seizing $8 billion from their bank account. That's still less than a year worth of profit for them, it won't make them go out of business. But it's enough that people will get the message quick.
Car companies have brazenly cheated emissions because the price of getting caught (nobody goes to prison, a few million dollars in fines) was far less than the money saved by cheating on emissions. If the price goes up, the equation changes.