This post isn't so much about who the Packers will pick over the next couple days but at what position.
2nd round. I thought about a wide receiver, but it doesn't make sense to draft one early when that would force them to release both Jeff Janis and Jared Abbrederis, instead of setting up a competition between the two in training camp. If not receiver, then there are a lot of outside linebackers expected to be drafted in the 2nd round. Utah State's OLB Kyler Fackrell wouldn't be much of a pass rusher but his ability to drop back in coverage might be very useful. He had a serious knee injury in 2014 but that probably wouldn't scare the Packers, who selected LB Jake Ryan last year despite his collegiate injury history.
If the Packers pick a defensive lineman and outside linebacker with their first two picks, they still need another linebacker, along with a defensive back, offensive tackle, and tight end. They might still draft a late round wide receiver and a late round quarterback to stash on the practice squad.
3rd round. This might still be the place to take another defensive lineman. Players like South Carolina State's DT Javon Hargrave and Nebraska's DT Maliek Collins aren't going to be available later in the draft.
4th round. The Packers are going to be busy at the end of this round because they have three picks during a period of 12 selections. Maybe Stanford OT Kyle Murphy is still available because he was limited by a quad injury during the combine workouts. Georgia Tech's DB D.J. White is about the same size as former Packers Casey Hayward and might be a future replacement as the nickel CB. Wisconsin's OLB Joe Schobert or Arizona's ILB Scooby Wright might be available for depth/future starter at linebacker.
5th round. Western Kentucky's TE Tyler Higbee might be another Richard Rodgers type of TE (he played as a receiver and TE in college). They could use another TE/FB for depth (it looks like John Kuhn is not coming back) or a future RB replacement for James Starks.
6th round. Maybe it's WR Moritz Boehringer time! He's almost the perfect candidate to draft, and let him spend a year or two on the practice squad learning how to play football.
7th round. Back in 2008, Ted Thompson probably didn't need to draft QB Matt Flynn in the 7th round but he liked his arm and didn't notice a bad thing about him. But otherwise he doesn't just select a QB at the end of the draft because he wants another arm in camp. He'd actually have to like a someone. Stanford's QB Kevin Hogan could be an option, if he falls in the draft due to legitimate concerns about his mobility and weird throwing motion.