What if you can only hand out $1M? Will someone still want to bribe you? -Of course, but he'll be a "smaller player" then.
All public spending involves some sort of "corruption" [1] because it's always other people's money being spent, and there's always someone in charge of spending it.
If you could pay $10 to get $100, wouldn't you do it? A bribe is an investment, and the tax money received in exchange is the ROI.
[1] I put "corruption" in quotes because it's just the system working as intended. If the system were actually corrupted, it would somehow start working for the masses' benefit instead.
Think about it. How do you benefit from someone else spending your money for you? Your money serves a means towards an end for whoever spends it, meaning he will be trying to benefit from spending it.