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But Democratic leaders in the Senate blocked all four of those bills Thursday, maintaining their insistence that either the entire government be funded or none of it will be funded.

“I, we, support veterans and parks and NIH and all these different elements of government that are closed. But we also are not going to choose between veterans, cancer research, disease control, highway safety or the FBI,” said Senate Majority Leader Harry Reid, Nevada Democrat.

Mr. Reid has reined in his chamber and rejected every House Republican proposal, but has offered no bills to break the logjam.

He and fellow Senate Democrats have said they will accept only one solution: that the House approve Senate-passed legislation that would fund basic government operations through Nov. 15 at an annualized rate of $986 billion. That bill is known in Washington-speak as a continuing resolution, or “CR.”

Sen. Schumer said there can be no negotiations with Republicans while the government is shut down because that would set a bad precedent.

“If we were to give in while the government was shut, to a demand, what do you think happens on the debt ceiling? What do you think happens when the CR has to be renewed?” Mr. Schumer said.

President Obama also tried to increase pressure on Republicans while speaking at a construction company in suburban Maryland.

“The only thing that is keeping the government shut down, the only thing preventing people from going back to work is that Speaker John Boehner won’t even let the bill get a ‘yes’ or ‘no’ vote because he doesn’t want to anger the extremists in his party. That’s all. That’s what this whole thing is about,” Mr. Obama said.

Democrats said the House, if it puts the Senate bill to a vote, would pass the legislation with significant Republican support and the crisis would end.

Mr. Cantor countered that it wasn’t clear the bill would pass, though he has refused to put it to a test.

Instead, House Republicans said that the individual bills they are passing would go straight to the president’s desk if the Senate approves them.

Mr. Reid said Democrats already have compromised by agreeing that the broad spending bill be written at an annualized discretionary spending level of $986 billion, which is tens of billions of dollars less than Democrats had planned.

He said Mr. Boehner agreed in a private conversation to pass a bill if it is at that level, and Mr. Reid indicated that Mr. Boehner has failed to live up to his word.