Senior White House officials hinted Sunday night at the battle to come in the next few months over tax and entitlement reform in connection with a deal struck between lawmakers and the administration to raise the debt ceiling to avoid a default on the nation’s debt.

The deal, which Senate leaders hope to bring to a vote Monday, would reduce the deficit by $3 trillion over the next 10 years via a two-step process. But the second step is bound to run into obstacles.

The first stage is composed solely of $900 billion in spending cuts, which would be paired with a debt ceiling increase of the same amount. The cuts would come from freezing discretionary spending over 10 years and would include $350 billion in cuts to defense spending.

A 12-member, bipartisan, joint Congressional committee would be charged with identifying the remainder of the deficit reduction measures and making a recommendation by Thanksgiving. Both the contentious issues of revenue raisers and entitlement reform would be under consideration.

“In this stage, everything will be on the table,” President Barack Obama said in brief remarks Sunday night after announcing the deal. “To hold us all accountable for making these reforms, tough cuts that both parties would find objectionable would automatically go into effect if we don’t act. And over the next few months, I’ll continue to make a detailed case to these lawmakers about why I believe a balanced approach is necessary to finish the job.”

The 2001 and 2003 tax cuts enacted by President George W. Bush, which Congress extended across the board after a similarly dramatic debate in December, are likely to be a part of the discussion.

Republicans want another extension for all income brackets, while Obama is pushing for an extension that excludes the wealthiest Americans. A White House official indicated that Obama could veto legislation that would extend all of the tax cuts.

“Faced with that decision, we hope Congress would make the right choice,” a White House official said.

The officials also said that Americans will be focused on the committee’s work and that Obama will not hesitate to call on them, similar to what he has done during the debt ceiling debate, to help influence the negotiations.

Congress has until Dec. 23 to act on the special committee’s recommendations. If either the committee or Congress fails to act, an automatic $1.2 trillion cut in spending for 2013 would be triggered. The cuts would be evenly divided between defense and non-defense spending, putting pressure on both parties to reach a deal.

Social Security, Medicaid and Medicare benefits would be exempt from the cuts.