Losing any game to Minnesota would have been a ranking nightmare.
Rutgers is definitely Iowa's last chance for any semblance of "statement" win(s). After that, any loss to teams ranked 127 or worse will likely undo any good achieved by beating those teams. Win 2/3 against Purdue and Indiana at home and Iowa will have negative RPI points for the weekend. Win 2/3 on road against Nebraska and MSU . . . same story.
If Iowa can finish 17-7 in the B1G and have 5 of those 7 losses come against Rutgers (if Iowa loses 2), Illinois (2 losses) and Michigan (1 loss), they'd have a good faith argument to make to get a regional bid so long as Michigan, Illinois and Rutgers finish in top 4. They'd probably need a strong tournament effort to bolster it.
Win 2 of 3 this weekend and some cushion is provided but I don't think that they can afford to drop any other series and likely need to sweep at least one, if not two.