Sharon Schorr, of suburban Cleveland, finally gave up on the federal exchange website after eight hours of failed clicks.
"It almost reminded me of going online and trying to buy Springsteen tickets," said Schorr, a self-employed accountant who works for her husband's recruiting firm in Orange, Ohio.
Others simply resorted to old-fashioned pen and paper.
Luis Veloz, 19, was so eager to have insurance that he had already mailed in a paper application by Tuesday night. He is hoping to avoid racking up major bills like his parents, who incurred $250,000 in debt when his father had a heart attack.
"It's an exciting moment because my family has never had preventative care," said Veloz, a college student.
Workers at the Florida Association of Community Health Centers printed out applications ahead of time.
"We don't care about the politics. This is about people so we were trying to make it easy for the patients," President and CEO Andy Behrman said.
Connecticut Gov. Dannel P. Malloy, a Democrat, said the law also known as Obamacare was working well because his state embraced the health reform law early on instead of fighting it. The state received 167 applications for coverage by the end of Tuesday.
"Because we took the time and effort to be ready, to handle the calls, to have our ducks in a row if you will, we are in far better shape than those states and governors that have turned their back on this historic program and historic offering," Malloy said.
The Obama administration hopes to sign up 7 million people during the first year and aims to eventually sign up at least half of the nearly 50 million Americans who are uninsured through an expansion of Medicaid or government-subsidized plans.
Many states predicted that an initial surge of interest would test the online system, but they expect most people to sign up closer to Dec. 15, the deadline for coverage to start Jan. 1. Customers have until the end of March to sign up to avoid tax penalties.
Under the law, health insurance companies can no longer deny coverage to someone with a pre-existing medical condition and cannot impose lifetime caps on coverage. They also must cover a list of essential services, ranging from mental health treatment to maternity care.