Bush's role in passing immigration reform

According to the WP, some House Republicans say that passage of a new immigration law is not possible unless President Bush puts all his energy into it.

One problem is that the last Bush approval rating I saw was 29 percent, just absurdly low (for a very cool graph of his approval ratings over time, check this out, compiled by Steven Ruggles at the University of Minnesota). Given the fact that immigration divides his party, the president has almost no incentive to use up what tiny amount of political capital he might have. There is thus a solid chance that nothing will be passed, though at this point there is pressure for Congress at least to look like it is doing something.

The Senate will likely vote on Thursday, and negotiations with the House will take place in June. Although I will be interested to see the Senate version, I wonder whether it will be relevant--either nothing will be passed or the ultimate law will scarcely resemble it given significant differences with House Republicans.