That's really cute of them but also really stupid. Democrats shouldn't give a fuck, and their constituents won't let them. Someone's misreading the opposition party if they think "calling their name" is going to cause a sense of responsibility or shame about these proceedings. Fuck these clowns. There can be no negotiation with people running a government like terrorists.
Besides. If Republicans are serious about coalition-style legislation, they'd have to fight off their right wing to do it. Are they really going to split their own party to make new legislation?
I doubt they'll do this but if they do offer to at least help stabilize the ACA then the dems really need to take it. Beyond that, though....