WASHINGTON — As the most diverse freshman class in history settles into the House of Representatives, newcomers like Alexandria Ocasio-Cortez of New York and Rashida Tlaib of Michigan have been racking up social media followers and soaking up the spotlight, liberal firebrands largely elected to safe Democratic seats.

But overlooked in the hallway protests and often glowing news media coverage, a larger group of more centrist Democrats has arrived with a different agenda. And now, they are quietly asserting their influence as the partial government shutdown, which has left them scrambling to explain why 800,000 workers are still without pay, enters its fifth week.

The centrists, elected to seats held last year by Republicans, delivered Democrats their House majority, and their re-elections will be critical to keeping the party in power. They include a sizable subset with backgrounds in military, intelligence and national security, and won by promising to work across the aisle and to end dysfunction in Washington. Now they are caught in the most dysfunctional situation of all — a record-breaking shutdown — and they are under pressure from constituents to do something about it.

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This past week, a group of freshmen in Trump-leaning districts convened a private strategy session to discuss how they could press Speaker Nancy Pelosi to reclaim the issue of border security for Democrats and to open the door to negotiations with President Trump. Some also aired their frustrations with Representative Hakeem Jeffries, the chairman of the Democratic caucus, who hosted a small dinner for freshmen from battleground districts.