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In three short weeks in office, Representative Alexandria Ocasio-Cortez has shaped a national conversation on taxation, emerged as the face of a green jobs plan in Washington and elevated her initials into a worldwide brand.

But she has not yet opened an office in her own New York City district — a delay that may give a sense of her priorities early in her tenure.

During an appearance on “The Late Show With Stephen Colbert” on Monday, she blamed the government shutdown.

“There’s a lot of things we can’t do as freshman members,” she told Mr. Colbert as they ate spoonfuls of ice cream. “We can’t properly set up our district offices. We can’t get laptops delivered. We can’t start doing the work that we were elected here to do.”