WASHINGTON — America’s poorest families would lose thousands of dollars in health benefits so that millionaires could get huge tax cuts under the Senate Republicans’ health bill, according to an independent analysis released Tuesday.

The study underscores the political difficulty of repealing and replacing Democrat Barack Obama’s health care law, which raised taxes on the rich while increasing health benefits for low- and middle-income families.

Families making less than $10,000 would lose, on average, more than $2,500 in annual benefits under the bill, once it is fully phased in. Families making more than $1 million a year would get

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