Sen. Chuck Schumer (D-NY), left, seen here speaking with Sen. John Barrasso (R-WY) in an elevator Sunday, says that undoing the sequester cuts is "one of the sticking points" in budget talks. Congress is struggling to find a solution to end the government shutdown, now in its thirteenth day. Andrew Burton/Getty Images hide caption

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Andrew Burton/Getty Images

Sen. Susan Collins, a Maine Republican, and fellow GOP senators accused the Obama administration of creating a "manufactured crisis" by furloughing FAA air traffic controllers and causing delayed flights. J. Scott Applewhite/AP hide caption

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J. Scott Applewhite/AP

Republican Sens. John McCain of Arizona, Lindsey Graham of South Carolina and Kelly Ayotte of New Hampshire at the Capitol last month. The senators are among a group invited to dine Wednesday with President Obama. Alex Wong/Getty Images hide caption

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Alex Wong/Getty Images

Under sequestration, federal agencies don't have the flexibility to choose to spare popular programs or services by making administrative cuts elsewhere. Tatiana Popova /iStockphoto.com hide caption

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Tatiana Popova /iStockphoto.com

Will the clouds part, the sun shine and a sequester solution be found? Jason Reed /Reuters /Landov hide caption

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Jason Reed /Reuters /Landov

NPR's Tamara Keith on where things stand

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House Speaker John Boehner held a news conference Feb. 13 in which Republicans promoted the hashtag #Obamaquester to blame President Obama for automatic spending cuts set to kick in March 1. Chip Somodevilla/Getty Images hide caption

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Chip Somodevilla/Getty Images

President Obama, accompanied by emergency responders — workers the White House says could be affected if state and local governments lose federal money as a result of budget cuts — speaks in the Eisenhower Executive Office building in Washington on Tuesday. Charles Dharapak/AP hide caption

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Charles Dharapak/AP

As he pressed Congress for action Tuesday, President Obama stood before a group of first responders. He made the case that their departments will be hurt if automatic budget cuts go into effect March 1. Win McNamee/Getty Images hide caption

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Win McNamee/Getty Images

Spending cuts that are part of the looming sequester could cause big job losses in defense and other industries. U.S. Navy/Getty Images hide caption

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U.S. Navy/Getty Images