A discharge petition means that if a majority of the House demands a vote, the vote will take place. And since it's widely acknowledged that there are more than enough votes in the House to pass the Senate bill, all you'd have to do is get those pro-reform Republicans to join Democrats in signing the discharge petition to make it happen.
Some Democrats are afraid that pushing a discharge petition could upset delicate bipartisan negotiations currently underway in the House. Others note that it's the best way to publicly put recalcitrant members on the record on the issue of immigration. And it's true! Absent a vote clearly feared by the xenophobes, the discharge petition forces individual members to publicly state whether they are for or against reform. Let fast-growing immigrant communities know exactly where the obstruction is coming from.
But don't get your hopes up. Even if a full-throated discharge petition campaign were launched, few if any Republicans would likely sign on. In essence, any Republican signatories would be ceding control of the chamber to the minority party, and you better believe the Republican leadership would severely punish any member that signed on.
So as a tool to actually pass a bill, a discharge petition would be as effective as House Speaker John Boehner's leadership style. That is, not effective at all. But as a tool to further pressure and embarrass Republicans? It would certainly work, and it would provide yet another news hook for Spanish-language media to keep pounding on Republicans.
Because right now, that's the only tactic reform proponents have left—try and embarrass Republicans into taking an action they'd clearly rather avoid.