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Analysts said the Obamacare publicity would have a “woodwork” effect, and people eligible for Medicaid would take notice of the exchanges and sign up for federal-state entitlements. But only the newly eligible population is covered by the federal government’s new contribution rate, meaning states would feel financial pain if the population that is currently eligible, even without Obamacare, enrolls at a higher-than-expected rate.

“The hardest reality about this trend is that the states haven’t budgeted enough for the new enrollees,” said Abigail Moncrieff, an associate professor at the Boston University School of Law.

Early Obamacare figures — to the extent they are available — might overstate the problem because people who already are eligible for Medicaid can get it now instead of waiting for Jan. 1, and trends could even out by the time open enrollment ends March 31 and improves.

Because Medicaid existed long before Obamacare, states were equipped to enroll the woodwork population faster than the expansion population or those seeking private plans on the exchanges, said Jenna Stento, a senior manager at Avalere Health, a Washington-based advisory firm.

“You are able to market and reach out to people under an existing program,” she said.