What is immigration amnesty?

The current immigration bill does give illegal immigrants amnesty.

Let's say the punishment for some crime is normally a $10,000 fine. If you receive amnesty then you don't have to pay the fine. What if, however, the government proclaims that (a) you must pay the government $5,000 and (b) the government will give you something worth more than $5,000. You have clearly received amnesty despite the fact that you must pay $5,000.

In general, a criminal has received amnesty if the combined punishments and rewards that the government gives them for having committed the crime make them on net better off. Since under the current bill illegal immigrants gain a considerable immigration advantage over those who didn't cross U.S. boarders illegally, and since this advantage is greater than any fine they must pay, the illegals will be receiving amnesty under the current bill.