It's been mentioned a few times in recent years. The illegal immigration situation in the US seems quite out of hand with no one really knowing how many there are and what they might be up to. Would a one-time granting of citizenship to illegal immigrants help the situation?

It might fix the situation or at least improve it a bit. However, only illegal immigrants who have proof that they worked and have not gotten into any problems should be granted with legal status. Citizenship would be a big extreme though, I think you meant to say legal residence. Once they have legally lived here for 5 years they can take the citizenship test and take a bigger role in the country (vote etc.).

The problem is that a lot of people would be outraged, but at the same time a lot of these people just came here to work hard, and not cause problems. And those who will be outraged, have to accept that fact, and learn to be more compassionate. A lot of these people come from poor countries or were in rough financial situations in their home country, and coming legally to the U.S doesn't happen overnight.