House aides are a bit wary since Schumer is newer to the fight and they were used to working with Kennedy.
House aides also point out they've held dozens of hearings on immigration, hearing from interested groups across the spectrum including labor groups and large employers. Those hearings haven't yet happened on the Senate side.
"We've said we can have something that can be ready to go whenever the president chooses, as soon as early this year," Schumer spokesman Brian Fallon told TPMDC.
White House aides have signaled key immigration players on Capitol Hill and in Washington-based interest groups that Obama is serious about pushing a comprehensive bill this year.
Sources tell TPMDC that Deputy Chief of Staff Jim Messina has talked to groups and lawmakers interested in immigration to say that it's possible the Senate could start debating a bill this spring.
But a House staffer warned, "Any time a White House makes a promise on legislation it's difficult because it's not up to them."
As we have reported, House Democrats refuse to vote on a bill until the Senate passes immigration, with members not willing to be caught again in a position where they vote on something politically untenable only to be told they have to accept a more conservative Senate version.
Late Update: White House Spokesman Nick Shapiro tells TPMDC:
"Senator Schumer has been a vital leader and tireless advocate for comprehensive immigration reform. We are greatly looking forward to working with him to finally fix this broken system."