Problem is, everything they've done so far has accomplished the exact opposite of that: By letting this thing linger, it is death by a thousand papercuts.
Or put another way: Either pass it or kill it dead once and for all. Because this current limbo isn't serving any Republican interests.
Remember, there isn't a single Republican who wants immigration reform. The only reason any of them are even considering it is because Latinos and Asians are the two fastest growing demographics in the country, and they're voting Democratic in overwhelming numbers.
Thus, you have Republicans on one side arguing that their party is doomed if current trends don't reverse, while other Republicans fear that making more brown voters will be the real cause of their demise. And right now, the two sides are stalemated.
As a result, Republicans get hammered daily in Spanish-language media for their recalcitrance, further eroding their stature in these critical growth communities. Remember, about 67,000 new native-born Latinos reach voting age every month. There's more at stake than the potential vote of 11 million undocumenteds. Lots more.
Furthermore, the nativists in the GOP aren't even in the mainstream of their own party. As one Republican pollster notes:
“Our research has shown that roughly one third of Republican primary voters will never support a path to citizenship no matter what the conditions,” says Ayres, a supporter of reform. “But two thirds will support a path to citizenship as long as the conditions are strict and rigorous.”Those "strict and rigorous" conditions are the same ones included in every single serious reform proposal, including the Senate bill: learn English, have a clean criminal record, pay back taxes and strengthen border security. The Senate bill more than qualifies, yet House Republicans balk at doing something supported by two-thirds of their own party.
And if you needed additional evidence, note that Republican primary voters didn't just nominate Sen. John McCain in 2008, and one-time immigration reform supporter Mitt Romney in 2012, but two of the three most popular 2016 possibilities support reform—Sen. Marco Rubio and Rep. Paul Ryan.
Republican voters simply aren't punishing Republicans who are pushing reform.
So if Republicans were smart, they'd pass the damn Senate bill. Or, they'd just kill reform altogether, rip off that band-aid, and hope that the public starts focusing on other things. Sure, Latinos would hate them, but at least they'd eliminate this daily reminder that Republicans hate them back.