One of the great falsehoods that the Gang of 500 seems to believe is that if Congress has the gall to challenge a president, the public will react negatively towards that Congress. This mostly comes from the republican led Congress' attempt to impeach Bill Clinton.
The problem with this line of thinking is that even during the great cum stain scandal, Bill Clinton remained a very popular president. Because of that popularity, there was a backlash. And I would argue that the backlash certainly wasn't catastrophic. Sure, a few guys got ran off Capital Hill, but most of them had their own keeping their pecker in their pocket problems. It certainly didn't lead to a wave style election like the one we saw last November.
In this case however, we have a very unpopular president who only the most extreme partisans support. The vast majority of the public are longing for the kind of investigations that the Democratic led Congress are starting to undertake.
These guys can't tell apples and oranges apart.