Senate Democrats today expressed mixed emotions about President Obama's health insurance fix before they headed into a closed-door session with White House Chief of Staff Denis McDonough to talk about the proposal to delay cancellation of policies that fall short of new standards.

Sen. Tom Harkin, D-Iowa, chairman of the Health, Education, Labor and Pensions Committee, said the president's solution is not the right answer and worriers that it will leave more people uninsured in the next year.

READ: Obama Announces Insured Can Keep Health Plans for a Year

"If I had been the president, I would not have done that. I think that as our investigation has shown that more and more of these canceled policies were junk policies and I don't think people realize they were paying good money for not even being covered," Harkin said. "But the president felt he had to do this, so he did it. We'll just keep working on it.

"It means for another year there will be a lot of people in our country that will not be covered," he added.

Sen. Joe Manchin, D-W.Va., who is co-sponsoring a bill with Sen. Mary Landrieu, D-La., to allow people to keep their health care plans indefinitely, said the president's announcement is "moving in the right direction."

"We've got to build this credibility back, and we've got to get people a chance that have had a policy to keep their policy," Manchin said. "It's a positive move in the right direction."

Manchin would not say whether he thinks there should still be a vote on Landrieu's plan.

READ: Boehner Predicts Obamacare Will 'Never' Work

Sen. Jeanne Shaheen, D-N.H., who is co-sponsoring a keep-your-plan bill with Sen. Mark Udall, D-Colo., said she favors a two-year transition period but is open to looking at the president's plan.

"I want to see if what the president proposed makes sense. We think we need a two year transition period, so that's what we're looking," Shaheen said.

But among the significant questions on Capitol Hill is whether the issue will still need a legislative fix rather than the administrative proposal presented by the president today. Sen. Chuck Schumer, D-N.Y., argued that an administrative fix is the only feasible solution because House Republicans won't support any "constructive" measure regarding Obamacare.

"The only way we're actually going to get things fixed it seems to me, as long as the House is intent on undoing Obamacare one way or another, is by the administration doing things on its own. So I think what the president did is exactly the right thing."

Several senators are likely to push for a vote on their own proposals, eager to show their constituents that they are trying to slow - and fix - Obamacare, their aides told ABC News.

"The president's announcement today was a great first step," Louisiana Sen. Landrieu said at a news conference this afternoon. "And we will probably need legislation to make it stick."