Because some of the Democrats were assholes. But so were all the Republicans who had supported it in the past, and who only opposed it (as proved by their continual opposition in later instances, no matter the procedural rules used by Reid) because their leadership demanded obstructing Obama as the greatest priority.
I wish Democrats had handled it differently – better tactics might have worked. But they tried to get it done – their mistakes and missteps on this issue are far, far less severe and significant than the Republican opposition. Based on polling, as well as discussions with pro-immigration voters (Latino and otherwise), the Republicans are the ones likely to suffer electorally for this issue. They don’t blame Obama because he was on their side, even if his tactics were less than perfect.
This makes some sense, especially in the primary. But looking towards the general, going after BLM activists for defending violent thugs who’s victims were black, like Bill was doing, is a winning tactic.