Updated: 3:01 p.m.

Senate Minority Leader Mitch McConnell (R-Ky.) said Sunday morning that his chamber was “very close” to reaching a deal to raise the debt ceiling via a $3 trillion package that would not include any tax increases.

“I think I can pretty confidently say that this debt ceiling increase will avoid default. … We’re not going to have job-killing tax increases in it. We are going to deal with this problem the American people sent us here to deal with, which is that the government has been spending too much,” he said on CNN’s “State of the Union.”

Director of the National Economic Council Gene Sperling, who also appeared on CNN, said the administration wants to delay any revenue-raising measures for the next 18 months while the economy recovers.

The package would raise the debt ceiling by about $2.4 trillion, which would cover the country through the 2012 elections. On the deficit reduction side, it would include about $1.2 trillion in immediate cuts to discretionary spending, then seek $1.8 trillion in further savings to be negotiated by a new bicameral, bipartisan Congressional committee tasked with recommending by Thanksgiving a framework for savings that includes entitlement reform. White House senior adviser David Plouffe, who appeared Sunday on ABC’s “This Week,” indicated that the committee would also look at revenue options.

The Senate will also vote on a constitutional amendment to balance the budget under this proposal, McConnell said.

“I think we’re very close to being in a position where hopefully I can recommend to my Members they take a serious look at it and support it,” he said.

McConnell and Senate Democratic Conference Vice Chairman Charles Schumer (D-N.Y) said the “trigger” — the mechanism built into the agreement to pressure the newly created panel to actually come up with a savings plan — is one of the elements still in flux.

“There should be a sword of equal strength and sharpness hanging over each party’s head,” Schumer said in a separate interview on CNN. “The preference would be some kind of revenue on wealthy people and loopholes. … Another possibility would be defense cuts of equal magnitude.”

McConnell said entitlement reform would be “absolutely critical” to the committee’s recommendations, while Schumer reiterated that Democrats would not tolerate cuts to Medicaid, Medicare and Social Security benefits.

Schumer said there would not be a short-term debt ceiling increase that would require another contentious vote several months down the road. 

“It is very vital to markets to have a long-term solution,” Schumer said, “so that we wont have to come back to this until 2013.”

But Schumer warned that Senate leaders have not finalized any deal. “There is no agreement,” he said. “No one has signed off on any agreement, so it’s premature to talk about any specifics.”