President Obama made it clear he would veto a short-term hike to the debt ceiling, expressing as much at a Thursday meeting with congressional leaders where three options for the size and scope of a package were discussed, according to a source familiar with the talks.

The option preferred by the president and Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) is to go big and approve a deficit-reduction package as large as $4 trillion, the source said.

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Obama thinks “they should go big and try to get the big one,” said the source.

At the White House briefing room this week, Obama urged lawmakers to seize a “unique opportunity” to cut into the national debt.

The short-term option of a $1 trillion cut in spending and hike to the debt ceiling is unpopular with Obama and Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE, whose conference would then have to vote more than once to raise the debt ceiling before the 2012 election.

Obama made it clear he would veto that option, which had been floated by Senate Minority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellIn rare move, Schumer forces vote to consider health care bill amid Supreme Court tensions COVID-19 talks hit crucial stretch Supreme Court nominee gives no clues in GOP meeting MORE (R-Ky.) and other Republicans, according to the source familiar with the talks.

Obama and the congressional leaders also discussed a second option that would cut spending by $2 trillion and raise the debt ceiling through calendar year 2012. A group of negotiators led by Vice President Biden had been discussing a package of this size.

“He did not dismiss that one,” the source said of the president.

House Majority Leader Eric Cantor Eric Ivan CantorThe Hill's Campaign Report: Florida hangs in the balance Eric Cantor teams up with former rival Dave Brat in supporting GOP candidate in former district Bottom line MORE (R-Va.) and Senate GOP Whip Jon Kyl (Ariz.), who both attended Thursday’s meeting, cast doubts about whether the big option could gain support and favored this middle option, according to a report Friday in The New York Times.

Both Cantor and Kyl participated in the Biden-led talks before pulling out over differences about whether a deal should include the elimination of some tax breaks.

A deficit-reduction package of $4 trillion would likely include increased revenue, raising pressure on Republicans to agree to eliminate some tax breaks.

Obama believes the big option could reduce the deficit to roughly 3 percent of gross domestic production, a level at which many economists believe the debt could be kept under control, helping to grow the economy.

House Democratic Leader Nancy Pelosi (Calif.) could also be a key player in the talks, given the fact that Republicans might need Democratic votes to move a measure through the House. She indicated Thursday that she could support a large deficit-reduction package, but said any changes to Social Security must be used to support that entitlement program and not to reduce the deficit.

Pelosi said she would not back cuts to Medicare or Social Security benefits.

Republicans have drawn a hard line on taxes, saying they will not agree to any tax increases as part of a deficit-cutting package.