House Republicans have agreed to set up a special conference committee in which the House and Senate can try to resolve differences over the government spending bill, but they won't be able to pass it before the government runs out of money and shuts down at midnight.

Barely an hour before the government was to partially shut down, the House began debate on the conference committee proposal only to have it rejected by Senate Democrats before the measure even reached the upper chamber.

Senate Majority Leader Harry Reid, D-Nev., said he would not support the House proposal because he had warned earlier that the Senate would not consider any bill that wasn’t limited to funding the government.

"We'd like to resolve issues, but we will not go to conference with a gun to our heads," Reid said.

The House has approved three measures so far that would have limited or derailed the new health care law, but Senate Democrats have rejected all of them.

Pressure is mounting on House Republicans to lessen the impact of a government shutdown that would start after midnight.

Passing a motion to go to conference with the Senate would shift the debate back to the Senate in the moments after the midnight deadline has passed.

Conference committees are used typically to resolve differences in legislation passed separately in the House and Senate.

"What we are attempting to do is get our people together," House Rules Committee Chairman Pete Sessions, R-Texas, said. "To actually have a conference."