President Barack Obama would like to see a comprehensive deficit-reduction package, but is exploring a possible fallback plan with congressional leaders to avert a debt default by Aug. 2, the White House said yesterday.

White House spokesman Jay Carney said that while Obama would prefer the biggest possible package, he is leaving room open for a safety valve to get an increase in the debt ceiling by Aug. 2, when the federal government will run out of money to pay its bills.

“We must pursue a fallback or last-ditch option,” Carney said.

He also said there must be a mechanism in place to ensure the United States does not default on its debt obligations.

Obama, who set a Friday deadline for lawmakers to reach a deal on the debt ceiling, held a secret White House meeting with Republican congressional leaders on Sunday — but there were no breakthroughs, a Republican congressional aide said.