The Senate on Wednesday is set to question Health and Human Services Secretary Kathleen Sebelius on the problematic rollout of the new health care law, but Senate Democrats have already begun to question the new program and push for changes or delays.

One of the law's staunchest Senate supporters on Tuesday declared that the implementation of Obamacare has become a crisis.

Senate Appropriations Committee Chairwoman Barbara Mikulski delivered a hefty dose of criticism to Marilyn Tavenner, Centers for Medicare and Medicaid Services administrator, who came to testify before a Senate panel about the health care law rollout.

"I believe that there's been a crisis of confidence created in the dysfunctional nature of the website, the canceling of policies and sticker shock from some people," Mikulski told Tavenner, adding that in her state, 73,000 individual insurance policy holders are facing cancellation because they do not offer the level of benefits required under the Patient Protection and Affordable Care Act, known as Obamacare.

The cancelled policies and website glitches have become a sudden and serious threat to an already vulnerable group of red-state Senate Democrats facing re-election in 2014.

One of those Senators, Mary Landrieu of Louisiana, on Monday introduced the "Keeping the Affordable Care Act Promise Act," which would allow individual policy holders to keep their current plans even if they don't meet the standards of the new law. Landrieu, who is running for a fourth term, wants to require insurers to inform policy holders about why their policy does not meet the new health care law requirements and what plans constituents could buy that might be better.

"We and the president said over and over again that if people have insurance and they like the insurance that they have they can keep it," Landrieu said when she unveiled her proposal.

Her opponent, Republican Rep. Bill Cassidy, is running an ad that declares Landrieu, who voted for passage of the health care law, "didn't level with you about Obamacare."

A second Senate Democrat, Joe Manchin of West Virginia, is pushing legislation that would delay the individual mandate to buy health insurance. Individuals and families have until March 31 to sign up on the new health care exchanges in order to be compliant with the law by January, but the website has been plagued with problems and is often unusable.

Eleven Democratic senators, eight of them up for re-election next year, have signed a letter to President Obama asking for an extension of the open enrollment deadline past March 31.

"Individuals should not be penalized for lack of coverage if they are unable to purchase health insurance due to technical problems," the letter states.

Some of the Senate's 55 Democrats on Tuesday withheld their support for either the Landrieu or Manchin bills, saying after a closed-door meeting that they wanted to focus on fixing the website glitches and watching what happens with the law as more time passes.

Senate Majority Leader Harry Reid, D-Nev., dodged a reporter's question about whether he would bring Landrieu's bill to the floor for a vote.

"You know, there are hundreds of bills introduced every week, and we have to sort through those that have opportunity to be voted on," Reid said.

Senate Minority Leader Mitch McConnell, of Kentucky, who is the the most vulnerable Republican up for re-election next year, said supporters are stampeding away from the new law.

"It'll be interesting to see when our Democratic friends both in the Senate and then at the White House begin to respond to the demands of the people of this country," McConnell said.