If we win our last 2 solidly, is there a chance we can make the top-12?
Let's look at it logically.
Assume a best case scenario, that winning handily will allow Illinois to be seen as the best 3-loss team per current record, passing Texas and Tennessee. Even in that case, though, they won't be ahead of any 2-loss teams at the end of the year. That, guaranteed, puts them behind Indiana, Ohio State, Texas A&M, Texas Tech, and Ole Miss. Despite the weakness of the ACC and Group of 5 teams, that takes away 2 more spots automatically.
Then we have the rest of the teams currently ahead of Illinois, and remember that they play each other. One of Oregon or USC will finish ahead of Illinois, at the least. So even assuming insanity happens elsewhere in college football, that's 9th at best.
Now, let's be realistic. Georgia has a game remaining against a terrible FCS Charlotte team, that aren't realistically losing that game, and a 10-2 Georgia team is ahead of Illinois even if they don't make the SEC championship.
From there, to make the playoff, Illinois would have to pass 9 of Miami/Georgia Tech/Virginia/Oklahoma/Alabama/Vandy/Utah/BYU/Notre Dame. Even if half of them completely collapse, ALL of them collapsing is such an unrealistic possibility, that Illinois is not a feasible option to make the playoff (not just less than 1%, more like less than 1% of 1%).