If Mankins doesn't sign his tender, he doesn't risk fines for skipping minicamp, which starts tomorrow, or training camp. He also wouldn't be subject to the 30-day rule, which states that players under contract must report by Aug. 10 (30 days to the NFL opener) to accrue the season towards free agency.
Mankins really wouldn't have to show until Week 10, though he would lose chunks of salary with each regular season game sat out, to have the season count towards free agency.
The downside, of course, is the cut in salary. But Mankins' feelings are likely similar to Jackson's -- If you have no intention of planning to play under the tender to begin with, then what does it matter if they cut that number?
It's also important to remember that it is, indeed, June. So there's time ... But for now, it looks like Mankins is at the end of his rope.