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“The president’s announcement presents a number of complex issues,” the state’s insurance administration said in a statement, adding that Maryland officials will meet with insurance companies and other parties to determine the best path forward.

New York’s Department of Financial Services, which oversees health insurance, didn’t respond to requests for comment Monday, but officials in the Empire State also reportedly haven’t made a decision.

Mrs. Warren — a first-term senator who quickly has become a progressive hero — is standing with the president and has defended the administration’s proposed fix.

“They’re trying to make the transition work. They’re trying to do everything they can to make it work and get people into the system,” she said last week after the president announced his proposed changes.

If health care reform does become a major issue in the Democratic primary, it likely would focus more on the management issues related to the website launch and other problems with implementation, rather the underlying goals of Obamacare, on which the potential candidates largely agree.

“I don’t think it’ll be a high-profile issue in which the debate moderators are trying to draw clear distinctions between one candidate and another, simply because I don’t believe there are clear distinctions to be had,” Mr. Scala said.