How to fight Minimum Wage hikes
Republicans! Want to fight the Minimum Wage increases that both Nancy Pelosi and Teddy Kennedy favor? Point out to Democrats that their quasi-open borders policies have driven down wages for low-wage workers, and that the best way to naturally raise the minimum wage is to reduce illegal immigration by low-wage workers. With fewer low-wage workers, there will be less competition for minimum wage jobs, and employers will have to offer more. Point out that a raise in the minimum wage would increase the numbers of illegal aliens working in the "cash economy", thereby driving large numbers of low-wage American workers out of work.
They'll probably respond with a tu quoque argument, at which point you admit that, yes, the GOP leadership is part of the problem and you're trying to do something about that. But, you then stress that it takes "two to tango", and that if the Democrats strongly opposed illegal immigration instead of supported it, the GOP would be forced to stop their support.
At the very least you'll create a log jam where the Dems are forced to choose between raising the minimum wage and reducing illegal immigration.