So, one positive aspect of raising the minimum wage is that it would decrease the amount of subsidies that these "workers" get from the government. If Wal-Mart or McDonald's pays a dollar more to an employee, that is a dollar less (in theory) the employee would get in food stamps - thus saving the taxpayers a dollar.
(Low-wage employers also love Obamacare, too. Rather than having to pay for health insurance, they make everyone a "part time" employee, and tell them to get federally-subsidized Obamacare. A minimum-wage employee qualifies for a full subsidy under Obamacare, so the Government ends up picking up the tab - transferring what was once an employer cost to the taxpayer! Again, government handouts to the poor end up being subsidies to big business!)
And maybe that is where the SEIU can get the GOP on board. Perhaps increases in the minimum wage can be tied to decreases in other subsidies, such as food stamps and the like. That would sell to both sides of the aisle.