WASHINGTON (AP) — If President Barack Obama, the House and the Senate all want to extend a Social Security payroll tax cut and jobless benefits through next year, why are they fighting so bitterly over doing it?

Obama, House Democrats and lopsided majorities of both parties in the Senate want to immediately renew the tax cut and jobless benefits for the next two months, and find a way later to extend them through 2012. House Republicans want to do it for a full year right away.

That doesn't sound like an unbridgeable gap. Yet the fight has evolved into a year-end partisan grudge match with no clear resolution in sight and with huge political and economic stakes.

Without action, the payroll tax paid by 160 million workers will rise by 2 percentage points to 6.2 percent on Jan. 1. That would mean $1,000 a year less in the pockets of people making $50,000, or about $19 weekly. In addition, 3 million people currently receiving long-term jobless benefits will begin to lose weekly payments that average under $300 — for many, their only support.

Following is a guided tour, in question and answer form, through the dispute.

Q: Why do Obama and the Senate want to extend the tax cut and jobless benefits by only two months?

A: Actually, they don't. When the Senate voted overwhelmingly last weekend for a two-month bill backed by Obama, it was a fallback position after Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., disagreed over ways to pay for a yearlong extension. Both sides agreed they would not let the bill increase long-term deficits.

The Senate's two-month version continues the payroll tax and jobless benefits at this year's levels and costs $33 billion. The bargainers agreed to pay for that by raising fees people pay for new mortgages or refinancing insured by Fannie Mae and Freddie Mac, the government-backed mortgage companies. For a $200,000 mortgage, the fee increase would raise a borrower's cost about $17 a month.

A full-year extension would cost around $200 billion, and the two sides couldn't agree on how to pay for that. So they agreed on a bill extending the tax cuts and jobless benefits through February, and then they would return early next year to resolve their differences over a yearlong measure.

Q: The government spends over $3.5 trillion every year. How hard can it be to find another $170 billion or so in savings?

A: It's been tough because of the math and the ways each side would do it.

The two parties seemed to agree that additional savings could come from a federal sale of parts of the broadcast spectrum, and by requiring government workers to contribute more to their pensions. Beyond that are vast differences, substantive and political.

A yearlong extension that the GOP-run House passed this month would make higher-income seniors pay more for Medicare coverage and cut spending for parts of Obama's health care overhaul law enacted last year. Democrats oppose both those provisions.

Democrats have proposed paying for a one-year extension of the payroll tax and federal unemployment benefits by imposing a 1.9 percent surtax on income above $1 million a year, a non-starter with Republicans. During talks between top Senate Democrats and Republicans, Democrats also proposed other ways of boosting levies on the wealthy, but those were rejected.

Q: Are there any other differences?

A: They're also fighting over the jobless benefits taxpayers should provide as the economy slowly improves.

Democrats want to keep the current structure. Most states provide 26 weeks of unemployment coverage, and federal programs enacted since the recession boost the eligibility up to 99 weeks in some states.

The House-passed bill would pare that total coverage to a maximum 79 weeks. That probably would fall even further in some states as employment improves. The House bill also requires benefit recipients without high school diplomas to pursue education alternatives and lets states test recipients for drug use.

Q: While they work through these differences, why the fuss over whether Congress first approves a two-month or a one-year plan?

A: For one thing, many freshman and conservative House Republicans are tired of compromising with the Senate and want their leaders to take a stand. They also say a two-month extension of the payroll tax cut would create uncertainty for taxpayers and businesses and problems for employers' payroll systems.

Many House Republicans hate the idea of keeping the issue alive until March 1, when the two-month bill would expire. Democrats have damaged Republicans politically with proposals to pay for the payroll tax cut by boosting levies on the rich. GOP lawmakers solidly oppose that approach, saying it would discourage job creation, and Democrats have used that to argue that Republicans are defending the wealthy at the expense of the middle class.

That's not an argument Republicans want to spend the 2012 election year having. As a result, many want to avoid additional votes on the matter next year, and they don't want to let Obama spend next month's State of the Union address discussing it. They would rather spend 2012 voting on issues they feel are on their terrain, like blocking Obama administration regulations, reducing the size of government and cutting its spending.

Q: What about Democrats?

A: They say the tax cut and unemployment coverage must be renewed to protect the millions who would be hurt Jan. 1. They also have no desire to surrender leverage by abandoning the two-month deal negotiated by the Senate's Reid and McConnell.

But they, too, have political motivations.

Democrats cite economists who say the payroll tax would pump enough money into the economy to help it grow slightly next year. Knowing that the 2012 presidential and congressional races are likely to hinge on the economy's performance, they want to take no chances with anything that might tip the economy in the wrong direction. To them, that means the payroll tax cut and extra jobless coverage must be extended.

Q: Wouldn't these bills also prevent a scheduled cut in reimbursements to doctors who treat Medicare patients?

A: Yes, a 27 percent reduction takes effect next month unless Congress acts. Doctors say that cut would discourage physicians from treating the elderly people served by Medicare. Neither party wants to anger older voters by limiting their access to doctors.