Ryan, chairman of the House of Representatives Budget Committee, has a string of earlier budget and tax proposals that could come under fire by Biden. The Democratic vice president is known more for his foreign policy experience, but he has played a major role in negotiating fiscal deals in the Obama administration.

Below is a brief summary of each campaign's recent positions and other tax issues that may come up.

BUSH-ERA TAX RATES

The most pressing challenge facing Congress is the December 31 expiration of lower income and investment tax rates enacted under President George W. Bush in 2001 and 2003.

President Barack Obama supports keeping rates the same for families making less than $250,000 annually. For income above that level, he favors raising the top two tax brackets to 36 percent and 39.6 percent.

Those rates are now at 33 percent and 35 percent.

Republican challenger Mitt Romney has called for extending all the Bush-era rates and wants to further cut all rates by 20 percent.

That has led to criticism that such cuts would cost $4.8 trillion over a decade, and debate over how Romney would make up the lost government revenue without adding to the deficit.

INVESTMENT INCOME

Obama wants to raise the dividend tax rate to match the ordinary income tax rate for the two highest income brackets. He also backs raising capital gains taxes to 20 percent from 15 percent for those brackets.

Romney wants to eliminate these taxes for households making less than $250,000 a year. In earlier budget proposals, Ryan has backed killing the investment taxes for all income groups, including the wealthy who tend to benefit most.

The 15 percent current investment tax rates for most taxpayers also expire on December 31.

Obama backs raising tax rates paid by private equity and other financiers, known as "carried interest," to the level of ordinary income tax rates, from their current 15 percent tax treatment.

Romney, whose net worth is estimated at up to $250 million after co-founding the private equity firm Bain Capital, has hedged on the issue. But nearly every Republican lawmaker including Ryan has voted against that change.

TAXING THE WEALTHY

Obama has also endorsed a "Buffett rule," named for billionaire investor Warren Buffett, to require households making more than $1 million a year to pay at least 30 percent of their income in taxes.

Both candidates back scrapping the alternative minimum tax, which puts a floor on the amount of taxes the rich pay.

Romney has said he will not raise the share of taxes paid by the wealthy, but he would target some of their tax deductions, perhaps setting a hard dollar cap.

TAXING THE POOR

Obama backs many tax credits used by the poor and working class such as the earned income tax credit and the child credit.

Republicans have criticized the expansion of many of the tax credits for poorer Americans and have tried to end some backed by Obama.

Romney ran into trouble when a secretly recorded videotape surfaced of him saying that 47 percent of voters were dependent on government and unlikely to support him.

Ryan in earlier budget plans has proposed eliminating nearly all special tax credits in exchange for lower tax rates.

CORPORATE TAXES

Obama backs cutting the top corporate income tax rate to 28 percent from 35 percent. Romney and many Republicans have proposed a rate cut to 25 percent.

Obama has offered a long list of corporate tax breaks to end, ranging from inventory accounting to interest on overseas profits and tax provisions benefiting oil and gas companies.

The president has said he wants to keep the current "worldwide" system of taxation where companies pay taxes on all profits, including those earned overseas.

Romney wants to exclude profits earned outside the United States from taxation, in a change to a system known as "territorial."

TAX CODE OVERHAUL

Obama and Romney say they back a complete tax code overhaul, but both have been vague on the thorny details.

Neither has explicitly embraced some bipartisan plans that call for lowering rates across the board in exchange for politically painful cuts to treasured tax breaks.

Romney backs the traditional mantra of lower rates and broadening the base of taxpayers, but has been less than specific on how he would achieve that.

Obama has not proposed a major tax overhaul either. And some Democrats say there is not enough revenue to lower rates for the wealthiest.

A major revamp of the tax code has not been done since 1986, under Republican President Ronald Reagan with a Republican Senate and a Democratic House.

(Reporting By Kim Dixon; Editing by Xavier Briand)