I was initially only going to look at the performance of replacement level defensemen to see if their inclusion in the lineup had any additional negative impact relative to that of losing a #1 or #2 defenseman. But I ended up pulling the "With or Without You" data for every defenseman over the last four seasons who played between 10 and 70 games in a season. That ended up being 502 in all.

I looked at two quantities: Even-Strength Save Percentage For and Even-Strength Save Percentage Against, both when the player was in the lineup and when he was out. I then regressed against average TOI. What we get is essentially this, with the coefficients varying slightly depending on how I weight the data:

Opponent's Save Percentage Delta vs Avg TOI = -0.44 * (TOI - 15)
Own Team's Save Percentage Delta vs Avg TOI = +0.44 * (TOI - 15)

TOI isn't a perfect proxy for a defenseman's ability (or for a team's performance when he's in the lineup), so we end up with R^2 in the range of 0.3 to 0.5. Nonetheless, replacing a good defenseman with a bad one tends to decrease your team's shooting percentage and increase your opponent's.