Updated: 1:47 p.m.

President Barack Obama challenged Republicans on Wednesday, saying that any package to reduce the deficit must take a “balanced approach” and that the GOP refusal to consider increased revenues is “not sustainable.”

Obama took his hardest line yet against Republicans that revenues must be part of a deal struck between him and Congressional leaders in the runup to the Aug. 2 deadline to raise the government’s debt ceiling. In his first question-and-answer session with reporters in four months, the president at times took a pedantic tone by pushing Democratic talking points on the budget — from “hard choices” to “leading” to the multiple mentions of corporate jet taxes.

“You cannot reduce the deficit the amount that we need to without having revenues in the mix,” Obama said, adding negotiators would need to trim the defense budget, “while still meeting our security needs,” as well as “tackle our entitlements.”

Obama also pushed back against the notion — floated by Republicans — that he has not been involved enough in debt talks, even though he dispatched Vice President Joseph Biden and other White House budget gurus to Congress to negotiate with leaders there. Obama noted he personally has met multiple times with leaders of both parties and held sessions with each individual caucus in each chamber for more than an hour each.

“At a certain point, they need to do their jobs,” Obama said. He added, “Now’s the time to go ahead and make the tough choices. That’s why they’re called leaders.”

The president’s remarks came nearly a week after collapse of those bipartisan talks led by Biden — negotiations that broke down because House Majority Leader Eric Cantor (R-Va.) and Senate Minority Whip Jon Kyl (R-Ariz.) walked away from the table over what they said was an impasse over taxes.

“Democrats have to accept some painful spending cuts that hurt our constituencies,” Obama said about cutting entitlements and government programs, before saying that Republicans also will have to negotiate about their “sacred cows” of revenues.

But Kyl said Obama’s statement that he was willing to look at entitlements like Medicare and Medicaid, was laughable given what happened during the Biden talks.

“We’re compiling a list of all the things that they have said are off the table. When they say they’re ‘open’ to talking about things … every time we tried to raise anything that was part of that they said, ‘sorry that’s off the table,'” Kyl said.

He also scoffed at Obama’s push to eliminate tax breaks for corporate jets. “If you’re having a conversation where you’re talking about something purely for political effect — corporate jets exclusion, which by the way they never raised with us — I ask you, is it serious or is it pure politics?”

But it’s clear the president doesn’t believe the Biden group’s work was for naught.

Obama said many on the Hill viewed the Biden talks as a “brush-clearing” exercise before others leaders stepped in. “Because of the work that has been done, I think we can bridge our differences,” he said, citing more than a trillion dollars worth of spending cuts that the group identified through nearly two months of talks. He called the common ground a “conceptual framework” for a final agreement.

But the concession that “progress was made” — a favorite refrain of Beltway insiders — did not stop Obama from laying down a marker for the next phase of deliberations, when he sits down with the four Congressional leaders and hashes out a deal. The president tried to paint the last leg of negotiations as a dichotomous choice: Either the deal will address revenues or the middle class will suffer at the expense of “millionaires,” “billionaires,” “corporate jet owners” and “hedge fund managers.”

“You’re still going to be able to ride on your corporate jet, you’re just going to have to pay a little more,” Obama said.

“If we chose to keep tax breaks … for oil and gas companies that are making hundreds of billions of dollars then that means we have to cut some kids off from getting a college scholarships … food safety might be compromised. … Medicare has to carry a greater part of the burden,” Obama added.

In the session with reporters, Obama cited the payroll tax holiday, which Republicans agreed to last winter as part of an agreement to extend the Bush-era tax cuts, as an example of bipartisan success in facilitating job creation. The White House has been considering another extension of a payroll tax holiday as part of the pending debt limit deal.

Obama is set to meet with Senate Democrats on Wednesday.

He insisted that both parties agree on the “scale and the urgency” of lifting the debt ceiling, even though some rank-and-file Republicans have referred to the debt limit as only a “technical thing.”

Obama said that he plans to meet with leaders of both parties and that his “expectation is that leaders are going to lead.”