Liberal Sen. Jeff Merkley (D-OR), who has co-sponsored Landrieu's bill, told TPM that Obama's move "doesn't go as far as I'd like it to go but it's a step in the right direction."
Sen. Kay Hagan (D-NC) also called the move "a step in the right direction" but likewise declared that "a one-year fix is not enough, and we need to do more."
Sen. Mark Begich (D-AK) told TPM he prefers a bill by Sen. Mark Udall (D-CO) to let people keep their insurance plans for two years. He added shortly after on CNN, "I think we have to move forward on the legislative plan." Obama's plan, he said, "is only as far as I can see, only a year long. I think, again, I think it's not enough, but it's a step."
"It's a step in the right direction and I'm not going to comment further on it," Sen. Jeanne Shaheen (D-NH), who backs Udall's bill, told TPM before entering a Democratic caucus meeting.
In a nationally televised speech Wednesday, the president announced he would allow -- but not require -- insurers to continue existing insurance policies for current policy holders, but not new customers, for one extra year. His directive would also require insurers to inform customers who choose to hold on to plans that don't meet Obamacare's minimum requirements about their options are under the law's insurance exchanges.
The announcement eased some of the panic over the law's botched rollout. Democratic senators roundly called it a step in the right direction. But it left some senators clearly unsatisfied, and that spells trouble for the White House and the party's leadership.
"This decision is sensible and provides the small number of affected consumers with more information and choices about their health care," Senate Majority Whip Dick Durbin (D-IL) said after a caucus meeting with White House officials. "There is no need for a legislative fix for this issue. Instead, Congress should continue to work with the Administration to improve the implementation of the law and redouble our efforts highlighting and explaining what this historic law will mean for 40 million Americans without insurance."
Senate Democratic leaders prefer to act administratively and do not want to modify Obamacare via legislation. They see as a last resort and worry it would open up Pandora's Box by encouraging Republicans to offer all sorts of amendments aimed at undermining the law. One leadership aide said there is no legislative fix to Obamacare cancellations that can pass both chambers of Congress. Democratic leaders also worry about setting a precedent of making legislative changes to the health care law before it's fully implemented.
"The fix proposed by President Obama today is an important step towards addressing a problem that has arisen," Senate Majority Leader Harry Reid (D-NV) said in an afternoon statement "and if we need to do more, we will."
Some Democratic senators agree with leadership that a legislative fix isn't needed.
"I don't want this to get tied up in the legislative process," Sen. Chris Murphy (D-CT) told TPM. "If the president has the ability to do this administratively, I think it's the right thing."
This article was updated at 4:12 pm ET.