Dems had a supermajority. They enjoyed widespread public support. Sarah palin made the loony right look pathetic. Obama was never afraid to overuse executive orders either - dems had a lot of levers to pull and a lot of leverage to pull them.
If they'd investigated the rampant illegality, that would've been very hard for a post-loss republican party engaged in in-fighting to defend against. A new generation of republican hopefuls would've been tempted to get air time by twisting the knife in the old losers.
Remember the hype around the special master under biden? Imagine that, aided by obama's charisma, with a super majority and before republicans completely corrupted the supreme court. They had a mandate and a lot of power.