No matter what the outlines are for a final agreement to lift the debt ceiling, the deal will include cuts to some of the nation’s major entitlement programs: Medicare, Medicaid and Social Security. President Obama signaled as much in his remarks Monday, when he said he was willing to accept reductions in programs Democrats have long protected and millions have come to depend on.

The details won’t be known until the final deal emerges — if there is a deal. But here are answers to some common questions about the options being considered.

What’s all this talk about cuts in Social Security benefits?

The president has been urging Republicans to agree to a “grand bargain” that would save $4 trillion over the next decade by combining big concessions on either side: Republicans would agree to higher taxes on the wealthy, and Democrats would agree to cuts in Social Security benefits, among other things. Congressional Democrats reacted warily, and House Republicans rejected the proposal outright.

But Obama has continued to press for a “big” deal, and some outside budget analysts say that even a smaller deal, in the $2 trillion range, would be difficult to make without resorting to savings from Social Security. The most likely form this would take is a technical adjustment to the formula used to calculate cost-of-living increases in benefits. Experts have long argued that the formula overstates inflation because it does not take into account changes in consumer behavior in response to rising prices.

Using a different formula, the “chained consumer price index,” would reduce the annual increase in benefits by, on average, about three-tenths of a percentage point, saving an estimated $112 billion over 10 years. The effect of the cut would grow over time — someone retiring at 65 could expect 3.7 percent less in benefits at 75 than under the current law, 6.5 percent less at 85 and 9.2 percent less at 95.

Social Security boosters worry about the impact on older recipients. But switching to the “chained” formula also holds appeal for liberals because it would bring in $87 billion in revenue over 10 years by revising income tax brackets — a tax increase that Republicans might accept because it is technical in nature and coupled with Social Security cuts.

Will Medicare beneficiaries feel any fallout from the cuts?

Yes. But first, some context, because there’s been an awful lot of back-and-forth over Medicare cuts. The 2009 health-care law signed by Obama trimmed $500 billion from the program, mainly by cutting subsidies to insurers selling Medicare Advantage plans and by reducing the rate of growth in payments to medical providers. Then came the House Republicans’ recent proposal to overhaul Medicare by replacing it with subsidies that seniors would use to buy private insurance coverage.

A debt deal will involve more Medicare reductions. The House GOP proposal would cut $250 billion from the program by, among other things, raising premiums for wealthier retirees, reducing payments for home health aides and raising co-payments for lab services. A major likely savings is restricting the Medigap policies seniors buy to supplement their regular Medicare, which fuel Medicare spending by making seniors less cost-conscious. Seniors who want the “first dollar” coverage that Medigap plans provide could instead be required to pay a supplemental Medicare premium.

Then there is the option of lifting the Medicare eligibility age from 65 to 67, which Obama has been willing to consider as part of a “grand bargain.” Many Democrats staunchly oppose this. But some experts note that such a switch would be more feasible once the health-care law is implemented in 2014, when people in their 60s with preexisting conditions should have an easier time finding affordable private coverage.

What will the impact be on the medical industry?

Substantial. Teaching hospitals are bracing for a cut in funding for graduate medical education. All hospitals could be forced to pay more for patient debts that go uncollected. Changing the government’s inflation formula would mean slower growth in some provider payments. And pharmaceutical companies, who fared very well in the 2009 health-care law, could be forced to give the government rebates for drug sales to people who are eligible for both Medicaid and Medicare, which would bring in an estimated $112 billion over 10 years.

Are people going to be cut from the Medicaid rolls?

They might. House Republicans have targeted Medicaid — the joint state-federal program for the poor, disabled and elderly — for major reductions, and Obama proposed cutting $100 billion over 10 years. The cuts could take the form of waiving the requirement that states maintain their current levels of eligibility, letting them trim their rolls. Or the cuts could take the form of a new formula for the federal government’s share of Medicaid costs that would leave the states paying more.

Because states are already burdened by Medicaid, this would probably lead to cutbacks in eligibility, to the extent allowed by Washington, and to cuts in already-low payment rates for doctors. These steps would greatly undermine the new health-care law, which calls for a big federally funded expansion of Medicaid eligibility in 2014, as well as higher Medicaid payment rates for primary-care doctors.

How did it come to this?

The entitlement programs face funding shortfalls in coming years, Medicare more so than Social Security. But many Democrats are dismayed that the programs are being targeted to close deficits that nonpartisan budget analysts say are driven in large part by the tax cuts passed in 2001 and 2003. Better, these Democrats say, to address the future entitlement shortfalls separately. But with Republicans refusing to consider tax increases, the entitlements are an obvious place to look for budget savings. And Obama appears eager to use the debt-ceiling talks to address the longer-term entitlement problem.