A colleague of mine who is really into politics (he watches MSNBC and FOX all the time, even while at work), thinks the Senate will turn Republican after the next election, and in the lame duck session Reid, in his last month as Senate majority leader will invoke cloture every 3 days to pass some 10 to 15 bills that have been held up by Grassley and others thus far. He thinks that they'll be Democrat supported measures in general, but will have to include a few that have bipartisan support. He doesn't think there are many bipartisan bills so HR 3012 could well be one of them that pass at that time. Otherwise he doesn't see Reid invoking cloture on something this unimportant to the American public. He thinks there is a good chance that if the economy keeps improving and Republican poll numbers keep dropping (apparently the most stated reason for independents to switch support is because Republicans are seen as obstructionists), then the Republican Senators who are up for tough reelections (not many with clout) and the entire Republican Congress (huge clout as a body) will give Grassley something else in return for his dropping his hold, just so that they can chalk up a successful immigration achievement that is still largely seen as their initiative. I asked him what they could possibly give Grassley, who has no reelection for another 4 years, no sign of credidble opposition and no obvious further ambitions, but he thinks there always is something.
This is purely one man's opinion. He has no inside knowledge of anything. He only knows about this bill because I've told him about it. What he has is decades of experience watching American politics, and a pretty good understanding (media driven no doubt) of what goes on in Washington. I believe him too.
In summary, I think the bill still has a 50-50 chance of getting through the senate unadultered (as it would happen not through cloture, but through Grassley dropping his hold) in the next several months, and a > 75% chance of passing at the end of the year.