House Republicans told Obama at the White House that they could reopen the federal government by early next week if the president and Senate Democrats agree to their debt-ceiling proposal. After the debt ceiling is lifted, a House GOP aide said they would seek some additional concessions in a government funding bill.

Obama repeatedly pressed House Republicans to open the government, asking them “what’s it going to take to” end the shutdown, those sources said. He questioned why the government should remain closed if both sides agreed to engage in good-faith negotiations on the budget, according to a Democratic source briefed on the meeting.

The meeting was described by both sides as cordial but inconclusive. Obama acknowledged to Republicans that notable progress had been made.