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That outburst, coupled with the Giffords shooting in 2011, helped spawn the bipartisan seating movement in the first place as a way to cool the heated debates in Washington.

Mr. Obama himself made that appeal as he opened his 2011 address, acknowledging Ms. Giffords’ absence and saying the shooting “reminded us that no matter who we are or where we come from, each of us is a part of something greater — something more consequential than party or political preference.”