White House Press Secretary Jay Carney said that Congress must reverse the spending cuts or induce “a constantly diminished sense of the greatness of America.”

Carney refused to take a government shut down off the table or admit that Obama might risk one in order to end sequestration, but he reiterated a demand for spending increases and tax increases that Republicans say amounts to a shut down threat.

“[Congress must make] responsible budget choices that include balance and a respect for the fundamental principle that the greatness of America is highly depending on the strength and greatness of the middle class,” Carney told reporters when asked if the government might shut down during this fall’s spending debate, “because the alternative is to see a constantly diminished sense of the greatness of America.”

Carney’s exchange with the reporter came after the office of House Speaker John Boehner, R-Ohio, faulted Obama for threatening to shut down the government.

“You see, last month, through a series of Statements of Administration Policy, the president announced that he would not sign ANY spending bills this year unless sequestration spending cuts are eliminated – and replaced with his plan for higher, job-destroying taxes,” Boehner spokesman Brendan Buck wrote in a blog post this morning. “The result of refusing to sign into law any spending bills, of course, would mean an unavoidable government shutdown.”

Senate Republicans have their own shut down threat in the works, focused on defunding Obamacare. “If congressional Democrats want to oppose appropriations bills without additional Obamacare funding, shut down the government, and side with the president and Big Business against the American people, then it’s their choice,” Sen. Mike Lee, R-Utah, who developed the proposal, told the Washington Examiner on July 9.

That idea has gained momentum over the last two weeks. “Lee said 15 Republicans have signed his letter and he expects the number will grow,” the Examiner’s Susan Ferrechio reported this morning. “He said 65 House Republicans have also pledged their support for the effort.”

Carney may have had Lee in mind when he transitioned from the question about the possibility of Obama shutting down the government to faulting Republicans for attempting to thwart Obamacare.

“What they don’t spend anytime on is an alternative,” he said.