Washington began bracing for a prolonged government shutdown on Tuesday, with House Republicans continuing to demand that the nation's new health care law be delayed or repealed and President Barack Obama and the Democrats refusing to give in.

There were signs on Capitol Hill that Republicans — knowing that blame almost certainly will fall most heavily on them — are beginning to look for ways to lift some of the pressure.

House GOP leaders pushed a new approach to end the impasse, offering to fund some parts of the government — including national parks, veterans benefits and the District of Columbia government. The goal was to put Democrats on the spot by trying to make them vote against programs that are popular among their constituents.