U.S. Sens. Mark Warner, a Virginia Democrat, and Saxby Chambliss, a Georgia Republican, are spearheading a new effort by more than a third of the Senate to prod their colleagues on a deficit-cutting supercommittee to make a much larger dent in the deficit as well as changes to entitlement programs and tax laws.

The bipartisan group of 36 senators, organized in recent weeks by Warner and Chambliss, urged the deficit-cutting panel Thursday to reduce the deficit by $4 trillion over 10 years instead of the planned $1.5 trillion.

The new coalition also wants the 12-member supercommittee to consider changes in the tax codes to generate more revenue, as well as changes to entitlement programs such as Social Security, Medicare and Medicaid.

"We want to say to the supercommittee, if they step forward, we've got their backs," Warner said.

In a joint news conference in Washington, the senators called on the supercommittee of six senators and six House members to borrow from detailed deficit-cutting plans and research already offered by the bipartisan Gang of Six senators, which included Warner and Chambliss, and the presidential debt commission. Both groups worked on proposals that included a combination of budget cuts, tax reforms and entitlement changes to cut close to $4 trillion from the federal deficit over 10 years.

Several senators said Thursday that the supercommittee, which by law must complete its work this fall to avoid automatic cuts in defense and other spending, doesn't have time to do its own extensive research.

"We know this debt is choking this country. And we feel it is time to check our political hats at the door and step up and do what is the right thing for the American people," Chambliss said.

Warner said it will be critical to persuade House members and private business leaders to also press the committee to do more than the minimum required.

Warner has argued that a deficit reduction plan will require some increase in revenues. He said during a speech in Virginia Beach last month that the tax rates could be lowered, but some deductions that are popular might end.

The new Senate coalition's statement wasn't specific on taxes but urged the supercommittee to develop "pro-growth tax reform."

House Republicans have long voiced opposition to raising taxes.

House Speaker John Boehner, R-Ohio, said in a speech Thursday that he supports changes in the federal tax code to make it "simpler and fairer to everyone," but he does not support any tax increases.

U.S. Sen. Jim Webb of Virginia, who is not part of the new coalition, told MSNBC on Monday that he opposes raising any income taxes but would look at changes in capital gains taxes and loopholes in the tax code. He said it's critical to encourage more private capital investment to revive the economy.

When asked about his views on the new Senate group, Webb spokeswoman Allison Jaslow said, "Sen. Webb fully agrees that we need to find ways to reduce the deficit."

The Senate coalition of 18 Republicans, 17 Democrats and one independent includes all of the Gang of Six except Senate Majority Whip Dick Durbin, D-Ill. However, Durbin attended the group's Thursday news conference in support.

Both North Carolina senators, Richard Burr, a Republican, and Kay Hagan, a Democrat, are part of the group.

Some senators, like Warner, supported the debt ceiling legislation last month that included the formation of the supercommittee, and others opposed the bill in some cases because they wanted deeper cuts. Several said they'll back the supercommittee's work regardless of their differences.

"It took two parties to get us $14 trillion in debt," said Sen. Kelly Ayotte, R-N.H., who voted against the debt ceiling bill. "And it's going to take two parties to get us out of this debt and this mess that we're in."