Washington (CNN) — The Obama administration will give more time to people who try to apply for health insurance coverage through the federal marketplace by Monday but encounter difficulty, administration officials said Tuesday evening.

Monday is the deadline for people to enroll in order to have coverage for this year or face penalties under the Affordable Care Act.

“Open enrollment ends March 31. We are experiencing a surge in demand and are making sure that we will be ready to help consumers who may be in line by the deadline to complete enrollment — either online or over the phone,” said Joanne Peters, a spokeswoman for the Department of Health and Human Services.

Administration officials said this move, similar to the one in December for the large number of people who were trying to sign up by January 1, will accommodate people who face special circumstances or complex cases and need extra time to complete their enrollment.

The officials said those who fall in this category will have to attest to their circumstances as part of the application process. They refused to say how much more time these people will get to finish enrollment and still qualify for coverage this year.

The Washington Post, which first reported the enactment of the new flexibility, said applicants would have until mid-April. Specific details could be released as early as Wednesday.

CNN last week reported the administration was considering this action. In an answer to a question from CNN Senior White House Correspondent Jim Acosta on Friday, White House Press Secretary Jay Carney indicated the administration would allow some flexibility for those who encountered problems meeting Monday’s deadline.

“As was the case for the December deadline, we’re going to want to make sure that people who are already in line can finish their enrollment,” Carney said.

Insurance industry sources did not want to comment in detail until they knew of the specifics but said anytime changes are made, it complicates their work and will require manual workarounds to help complete applications. They said so long as the time period is limited, they can accept it.

Republicans Tuesday evening criticized the move by the administration.

“Another day, another Obamacare delay from the same Obama administration that won’t work with Republicans to help Americans suffering from the unintended consequences of the Democrats’ failed health care law,” Republican National Committee Chairman Reince Priebus said in a statement.

The White House is trying to meet a goal of enrolling 6 million people. As of mid-March, 5 million had enrolled. The administration has been engaged in an exhaustive effort to not only enroll as many people as possible but also to increase the percentage of young adults who apply to help balance the makeup of those insured.

The administration said it has recently seen a major increase in traffic to HeatlhCare.gov. On Monday the site logged 1.1 million visitors, its second-busiest traffic day.