Will the House act? The Hill shows some of the mixed and murky signals being sent:

House Democratic leaders have suggested that they will not act on a broad immigration reform bill unless the Senate acts, a remote possibility following last week’s failed cloture vote
House Republican leaders are calling out their Democratic counterparts for failing to tackle immigration matters, but have made it clear they do not want the lower chamber to act on President Bush’s proposed guest-worker program.

Kurt Bardella, a spokesman for Rep. Brian Bilbray (R-Calif.), who chairs the House Immigration Reform Caucus, said the demise of the Senate bill was a positive development for border security and the debate forced Congress to “come to grips with the reality that the illegal immigration issue is an issue of national importance.”

While "Minority Whip Roy Blunt (R-Mo.) said he expected many of his members to line up behind a bill crafted by King and Rep. Lamar Smith (R-Texas), ranking member on the Judiciary Committee,"

Some House Democrats, meanwhile, want to move forward on comprehensive immigration reform.
Following the Senate vote last week, Rep. Zoe Lofgren (D-Calif.), who chairs the House Judiciary Subcommittee on Immigration, Citizenship, Refugees, Border Security and International Law, said in a release that Democratic leaders need to “improve the current unsatisfactory system.”