People who've started applying for health insurance but aren't able to finish before the March 31 enrollment deadline will get extra time, the Obama administration announced Tuesday.

"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," Health and Human Services spokesman Aaron Albright said.

The White House is scrambling to meet a goal of 6 million signed up through new online markets that offer subsidized private health insurance to people without access to coverage on the job. The HealthCare.gov website got more that 1 million visitors Monday, and the administration also wants to prevent a repeat of website problems that soured consumers last fall.

Officials said the grace period will be available to people on the honor system, meaning applicants will have to attest that special circumstances or complex cases prevented them from finishing by March 31.

It's unclear how long the extension will last. Some have urged the administration to allow until April 15, the tax filing deadline. People who are due refunds may be willing to put some of that money toward health care premiums.

During a March 12 congressional hearing, HHS Secretary Kathleen Sebelius told Texas Republican Rep. Kevin Brady that there would be no such extensions.

'Are you going to delay the open enrollment beyond March 31?' Brady asked.

'No, sir,' she replied.