[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2010/images/01/28/art.landrieu.0129.gi.jpg caption="Landrieu takes swipe at Obama over health care."]
(CNN) - President Obama is taking heat from a Senate Democrat over how he dealt with the issue of health care in his first State of the Union speech.
"I think the president should have been more clear about a way forward on health care last night," Sen. Mary Landrieu told reporters on Capitol Hill Thursday. "I'm hoping in the next week or two he will be, because that's what it's going to take if it's at all possible to get this done."
"Mailing in general suggestions, sending them over the transom is not necessarily going to work," the Louisiana Democrat added.
Obama didn't address the signature issue of his first year in office until about halfway through the 71-minute speech, and then only discussed it for about five minutes. But he urged Congress not to abandon the effort that now appears in limbo following the Democratic Party's recent loss of its supermajority in the Senate.
"Do not walk away from reform. Not now," Obama said. "Not when we are so close. Let us find a way to come together and finish the job for the American people."
Landrieu, one of the last members of her party to agree to the final Senate health care bill, also suggested the president erred in allowing three separate Senate and House committees to pass various versions of the bill.
"As far as I know, the president thought it was a good idea to have three different bills debated," she said.
"No wonder people got confused. So it's not completely our fault that that was the plan."
Landrieu also said she felt the president unfairly blamed the Senate during his speech for holding up a series of initiatives that had already cleared the House.
"I thought he was pointing his finger at the Senate a lot throughout the speech last night … no I do not think its fair," she said. "Moderate Senate Democrats, who give the Senate the 60 votes, come from states that have to appreciate a broad range of ideas and since the president ran on a bipartisan, change, working with Republicans, [he] doesn't do a great service to then say everything the House passes without any Republican votes is something the Senate should just take."
- CNN's Ted Barrett and Alexander Mooney contributed this report