The pressure is on for the federal government and states running their own health insurance exchanges to get the systems up and running after overloaded websites and jammed phone lines frustrated consumers for a second day as they tried to sign up for coverage using the new marketplaces.

In some ways, the delays that persisted Wednesday were good news for PresidentBarack Obama and supporters of his signature domestic policy achievement because the difficulties showed what appeared to be an exceptionally high level of interest in the overhauled insurance system. But if the glitches aren’t fixed quickly, they could dampen enthusiasm for the law at the same time Republicans are using it as a rallying cry to force most of the federal government to shut down.

“I’m anxious to see what the insurance is going to look like for my family at the beginning of the year,” said David Berge, a pastor with two young children in Shoreview, Minn., who tried unsuccessfully at least 10 times to create an online account on the state-run site MNsure. His high-deductible plan expires at the end of the year. . .