President Obama in a private meeting at the White House Wednesday was on the receiving end of complaints from Democrats frustrated with the botched rollout of Obamacare's public exchanges.

Senate Democrats up for re-election in 2014 grilled the president as problems persist with and the administration remains on the defensive for claims that all Americans could keep their health plans under Obamacare.

“It is simply unacceptable for Alaskans to bear the brunt of the administration's mismanagement of the implementation of the Affordable Care Act and that is the message U.S. Senator Mark Begich delivered to President Obama today,” the Democrat's office said in a statement sent to reporters.

Also attending the meeting were Democratic Sens. Cory Booker, N.J.; Chris Coons, Del.; Dick Durbin, Ill.; Al Franken, Minn.; Kay Hagan, N.C.; Mary Landrieu, La.; Jeff Merkley, Ore.; Mark Pryor, Ark.; Jack Reed, R.I.; Jeanne Shaheen, N.H.; Brian Schatz, Hawaii; Mark Udall, Colo.; Tom Udall, N.M.; Mark Warner, Va.; and Michael Bennet, Colo. Bennet is chairman of the Democratic Senatorial Campaign Committee.

A White House official said the meeting was conducted so the president could “hear their input on existing challenges” with implementing the health law.

“The president emphasized that he shared the senators’ commitment to ensuring that Americans who want to enroll in health insurance through the marketplaces are able to do so in time for insurance to start as early as Jan. 1, and throughout the open enrollment period which goes through March 31,” the White House official said.

The meeting was not listed on the president's public schedule.

Some of the Democrats at the White House Wednesday were none too happy with the progress made thus far by the administration.

“Consumers should have the time they need to shop for a plan and enroll after the widespread problems with the website are fixed. I urged the president again to extend the enrollment period to give consumers enough time to make an informed decision about their family's health insurance options," Udall, the Colorado senator, said.

In a hearing on Capitol Hill earlier Wednesday, Health and Human Services Secretary Kathleen Sebelius told lawmakers that the first batch of enrollment figures in the public exchanges, to be released next week, would be “very low.”