Obama and Democrats want to eliminate tax breaks and loopholes worth about $600 billion over 10 years as part of a broader $1.2 trillion deficit-reduction package that would include entitlement reforms.
Some Republicans have indicated support for ending such tax breaks as part of a broad deal. However, the fiscal-cliff agreement in January that resulted in higher tax rates on top income earners galvanized opposition by GOP leaders to further increases in tax revenue.
Meanwhile, Republicans say Obama and Democrats must deliver on significant entitlement reforms.
One change Obama has proposed would tighten the adjustment for inflation of benefits such as Social Security, meaning annual increases for future recipients would grow at a slower pace.
Opponents of the reform, known as "chained CPI" in reference to the Consumer Price Index it involves, argue it hurts senior citizens and others who most need their benefits.
If achieved, a grand bargain would give Obama a major political victory and a boost in cementing his desired presidential legacy after the controversial health care and Wall Street reforms of his first term.
Republicans also would get credit from moderates and independents for a willingness to compromise, but conservatives could punish them with primary challenges in 2014 and beyond.
Another possible outcome is a limited agreement that would include some elements under discussion.
For example, a smaller agreement might end some tax breaks and loopholes while cutting Medicare costs paid to providers, not beneficiaries, to achieve $500 billion or so in deficit reduction over 10 years.
Such a result, coupled with previous spending cuts and the January fiscal-cliff deal, would fail to reach the total $4 trillion in deficit reduction over the next decade that economists and political leaders have targeted as the minimum amount needed.
It also would allow both parties to simultaneously claim credit for making some progress while continuing to blame the other for preventing more.
A status quo outcome -- no major deficit reduction steps -- would mean continued brinksmanship over each pending fiscal deadline, as well as further economic uncertainty that already has lowered the U.S. credit rating and slowed growth.