Even as the White House and congressional Republicans brawl over the so-called fiscal cliff that could devastate the nation's economy, both sides started a second partisan feud Thursday over whether to raise the government's borrowing limit, further complicating an already muddled negotiation.

President Obama is insisting that any deal reached to avoid the fiscal cliff -- a blend of across-the-board tax increases and massive federal spending cuts set to begin in January -- should also include an increase in the nation's debt ceiling, the amount the government can borrow to maintain its operations. The government is set to reach its current $16 trillion limit in a matter of months.

Treasury Secretary Timothy Geithner, the president's point man on the current negotiations, went to Capitol Hill on Thursday with a proposal that called for a permanent increase in the debt limit.

But Republicans quickly rejected the White House's offer.

House Speaker John Boehner, R-Ohio, who battled with Obama last year over raising the debt ceiling, said Republicans won't agree to another hike without corresponding spending cuts at least equal to the increased borrowing authority. The White House called Boehner "deeply irresponsible" for insisting on deeper cuts in programs that will already be reduced by any deal on the fiscal cliff.

"Asking that a political price be paid in order for Congress to do its job to ensure that the United States of America pays its bills and does not default for the first time in its history is deeply irresponsible," said White House press secretary Jay Carney.

The exchange highlights the complicated and seemingly deadlocked state of negotiations involving a number of moving pieces and two sides whose positions only have hardened in recent days.

Publicly at least, both sides appear to have dug in. Republicans fear another debt-ceiling increase would amount to a blank check for a federal government that has yet to deal effectively with its runaway deficit. Democrats counter that Republicans are obstructionists putting the nation's fiscal health in danger.

Neither side wants to be blamed for allowing tax increases and sweeping budget cuts to hit Americans still reeling from the recession in the New Year. A recent CNN poll shows 45 percent are ready to blame Republicans if a compromise isn't reached; 34 percent would blame Obama.

Still, expanding the negotiations on the fiscal cliff to include a deal on the debt limit could give Boehner and Republicans additional bargaining power as long as they are able in the end to reach a deal, analysts said.

"Right now, it's the best single weapon in his arsenal; it's the wild card," said Republican strategist Ford O'Connell. "But he has to realize that if we go over the fiscal cliff, it appears most Americans are going to place the blame on the Republicans."

Lincoln Mitchell, of Columbia University's Harriman Institute, agreed.

"They have nothing to lose by pushing Obama this way," Mitchell said. "This is a president who may negotiate a lot away. The Democrats, at least under Obama, have been flummoxed about what to do with this Republican argument [on the debt ceiling.]"