[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2010/images/03/07/art.vanhollen0307.cnn.jpg caption="Democratic Rep. Chris Van Hollen, center, said Sunday that his party does not currently have 'a mortal lock' on the necessary votes to pass health care reform in the House."]
Washington (CNN) - Despite a call from the White House for health care legislation to pass this month, key Democrats on Sunday avoided any promises about how soon the next steps may come.
"I believe it will pass. Do we have a mortal lock? No," Rep. Chris Van Hollen, chairman of the Democratic Congressional Campaign Committee, told CNN's "State of the Union."
Questions remain about specifics of the final legislation, and until then "it's going to be hard to get people to commit" to a vote in the House, he added.
The president's own secretary of Health and Human Services skirted repeated questions about the timeline set by the White House.
"I think the president has called for an up or down vote. I'm confident that we'll have that up or down vote," Kathleen Sebelius told NBC's "Meet the Press." Pressed about whether the president would come back to the legislation if it does not pass this month, she responded, "I think it's realistic because the American people are desperate for something to help them."
She added, "the time clock is not about... a Congressional tick-tock - what Americans want is something to be done."
The administration has called for the sweeping legislation to be at the president's desk before the Easter vacation at the end of the month. And it has set an even earlier date for the House to vote on the Senate's version of the bill - one of two major steps in passing the bill.
"The president leaves for Indonesia and Australia on March 18th, and... I believe that, based on conversations that I've had in the building, that we're on schedule to get this through the House by then," White House spokesman Robert Gibbs told reporters Thursday.
The second major step in the Democrats' strategy - having the Senate vote on a separate package of amendments to the bill through a simple majority vote using a process called budget reconciliation - would "come closely thereafter," Gibbs said.
Gibbs added that he was "not setting a deadline," but going by conversations with people about a schedule.
Two Democratic leadership aides told CNN last week that House Speaker Nancy Pelosi is aiming to have the House complete its action by March 17. They said language in the legislation would be posted in the coming days, and that final language would be available 72 hours before a vote.
Deadlines come and gone have been a staple of President Obama's efforts to push through health care reform. "State of the Union" on Sunday ran a montage of clips of the president from the past year, first calling for a final bill "before the August recess," then for getting "health care done by the end
of this year."
But the latest prodding is unlikely to trigger the kind of rush the White House wants.
"People are still looking at some of the changes that are being made to the bill," Van Hollen told "State of the Union."
He added that "until people have a final product that they are able to look at and the Congressional Budget Office, our referee on budget issues, says whether or not this will do what the earlier bills did, then I think it's going to be hard to get people to commit."
Fellow Democratic Rep. Brian Baird, D-Washington, remains undecided about whether he will support the legislation. A practicing neuropsychologist before being elected to Congress, the retiring congressman told CNN he applauds the president and the party "for taking this difficult challenge on."
"The question is: Is this the best way we can do reform? And it is very complicated. It will be expensive, though to its credit, both bills, the House bill and the Senate bill, will be largely paid for and actually reduce the deficit over time," he said, adding that he "would have approached it perhaps a good bit differently."
The Senate's top Republican, meanwhile, made clear his party won't relax any of his efforts to halt the reform package however it can.
"What the American people would like us to do is not make this gargantuan mistake, in spite of Secretary Sebelius' best efforts," Senate Minority Leader Mitch McConnell told ABC's "This Week."
And if the bill does go through, avoiding a Republican filibuster in the Senate by using the reconciliation tactic, the battle moves to its next stage.
"Every election this fall will be a referendum on this bill," McConnell warned.
Updated: 3:02 p.m.