The President released a video Tuesday night rallying supporters of Obamacare and encouraging citizens to enroll in Obamacare via methods other than their website, which is being criticized for its design and structure.

Editor’s note: This story has been edited to correct information about the health care deadline. The White House says March 31 has always been the intended deadline to sign up for health care to avoid a tax penalty.

The White House reaffirmed a key deadline in the health reform law Wednesday, saying people have until March 31 to sign up for health insurance even if the coverage doesn’t kick in till later.

The Obama administration is being pushed to soften some of the law’s requirements, including the so-called individual mandate – the requirement that just about everyone have some sort of health insurance starting next year.

Separately, Democratic Sen. Joe Manchin of West Virginia was already drafting a bill earlier Wednesday to delay the mandate for a year, his spokesman said. And Sen. Jeanne Shaheen, D-NH, on Wednesday called for an extension of the open enrollment period to allow people more time to purchase coverage; Democratic Sen. Mark Pryor of Arkansas said he supported Shaheen’s “common sense idea” in a statement.

But the White House said late Wednesday it was standing firm on one of the dates – the deadline for open enrollment on the health insurance marketplaces, one of the main pillars of the 2010 Affordable Care Act.

“In the Marketplaces, you have to sign up by the 15th of a given month in order for health insurance to start on the first day of the next month,” the White House said in a statement. "As a result, some have asked whether consumers could face a tax penalty if they don’t enroll in coverage by Feb. 15th of next year. This is not the case. If you sign up for insurance by the end of March, you will not face a penalty."

This deadline clarification is unrelated to the rocky roll out of the online exchanges, according to administration officials.

AP Photo/ Evan Vucci Health and Human Services Secretary Kathleen Sebelius seen arriving in the Rose Garden of the White House, Monday.

Other critics of the health care law, including Sen. Marco Rubio, R-Fla., have proposed delaying the individual mandate penalty until six months after the Government Accountability Office certifies that the problem-plagued health care website is working.

The Department of Health and Human Services also announced Wednesday that it will hold daily briefings to update reporters on the progress of what President Barack Obama has called the “tech surge” to rectify the hitches and glitches on the troubled health care website.

The daily briefings will start Thursday, just two days after Health and Human Services Secretary Kathleen Sebelius said Obama did not know about the health insurance website’s hitches and glitches until after it was launched three weeks ago.

NBC News’ Chuck Todd, Michael O’Brien, Maggie Fox and Tracy Connor contributed to this report.

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