RICHMOND, Va.—A bipartisan group of senators is close to proposing legislation they hope will force Congress to tackle the federal government's ballooning debt, and they have begun a road show to win public support.

The proposal would cut the federal budget deficit by $4 trillion over 10 years, roughly four times the savings the White House proposed in February, Sens. Mark Warner (D., Va.) and Saxby Chambliss (R., Ga.) told about 200 business leaders at a meeting in Richmond.

If enacted into law, the plan would likely force Congress to boost revenue through new tax rules, cut spending and bring down the growth rate of Medicare and Social Security over time.

Some executives at the meeting appeared skeptical that a bipartisan deal could eventually win support from Congress and the White House, but many encouraged the lawmakers to try.

"They know they have to do it now and if they don't do it now, we are going to have other countries in charge of our future," said Doug Gray, executive director of the Virginia Association of Health Plans trade group, who attended the meeting.

Messrs. Warner and Chambliss are crafting the proposal with Majority Whip Richard Durbin (D., Ill.), Budget Committee Chairman Kent Conrad (D., N.D.), Tom Coburn (R., Okla.), and Mike Crapo (R., Idaho).

Mr. Warner's presentation showed that if current trends continued, interest payments on federal debt would skyrocket from more than $20 trillion in 2060 to $80 trillion in 2080. It also showed that U.S. government debt as a percentage of total economic output could soon equal that of Greece, whose fiscal problems have threatened to destabilize Europe.

"If we put this off, we are approaching financial Armageddon," Mr. Warner said.

The senators said their plan would seek to largely implement the recommendations made in December by the White House's bipartisan deficit-reduction commission. That group called for cutting spending in myriad government programs, and trimming costs on Medicare, Medicaid, and Social Security. The proposal was made by commission co-chairmen Democrat Erskine Bowles and Republican Alan Simpson.

Messrs. Warner, Chambliss and their colleagues are considering whether to set mandatory numerical targets for spending and revenue, and leave it up to individual congressional committees to determine how to hit them. Failure to meet the goals could trigger automatic tax increases and budget cuts.

The lawmakers didn't say how long the committees would have to hit their prescribed targets before the tax and spending "consequences" would kick in. In this way, the plan would spread the responsibility for deficit reduction across enough entities that they would collectively be able to withstand the opposition any deal might trigger.

"The only way we're going to get this done is for everybody to have skin in the game and everybody to get their ox gored a little bit," Mr. Chambliss said.

Aides said talks remained fragile, particularly as Messrs. Chambliss and Warner tried to broaden support for a plan in a Congress deeply divided on tax and spending matters. The lawmakers have worked for months to reach a deal, but had revealed little about their goals and strategy until Monday.

At the event in Richmond, Messrs. Warner and Chambliss repeatedly defended controversial parts of the Bowles-Simpson plan. That plan would, among other things, curb defense spending, limit the mortgage-interest tax deduction, and raise the age for drawing full Social Security benefits from 67 to 69 over several decades.

The talks come as House Republicans say they will include goals for restraining entitlement growth in their 2012 budget, to be released in April. But House Speaker John Boehner (R., Ohio) said GOP lawmakers also will launch a public education campaign on the programs' soaring costs.