Defending the shaky rollout of his healthcare law, President Barack Obama said frustrated Americans "definitely shouldn't give up" on the problem-plagued program at the heart of his dispute with Republicans over reopening the federal government.

Obama said public interest far exceeded the government's expectations, causing technology glitches that thwarted millions of Americans when trying to use government-run health care websites.

"Folks are working around the clock and have been systematically reducing the wait times," he said.

The federal gateway website was taken down for repairs over the weekend, again hindering people from signing up for insurance.

With no sign of a breakthrough to end the government shutdown, Obama said he would be willing to negotiate with Republicans on healthcare, deficit reduction and spending — but only if House Speaker John Boehner (R-Ohio) holds votes to reopen the government and increase the nation's borrowing limit.

Some House Republicans are seeking healthcare concessions from Obama in exchange for approving government financing and want more spending cuts before raising the debt ceiling.

The deadline for keeping the government open coincided with the Oct. 1 start of sign-ups for the insurance markets at the center of the healthcare overhaul Obama signed into law during his first term. Government websites struggled in the first week to keep up with high demand for the new marketplaces. It's not clear that more than a few managed to enroll the first day.

Obama said he didn't know how many people had enrolled. Administration officials have said they do not plan to release real-time data on the number of people enrolling, though some states running their own exchange websites are doing so.

The president predicted that when the six-month signup window for the insurance exchanges ends, "we are going to probably exceed what anybody expected in terms of the amount of interest that people had."