Palestinian polls show Abbas gaining significant support in recent months over Hamas, which harshly criticized his willingness to meet the Israeli leader without a settlement freeze in place.
A majority of Israelis support a two-state solution, including steps such as a settlement freeze.
The South says it is tired of an approach that lets North get perks for small concessions.
China is due to unveil a new proposal at the gathering Tuesday, but its plans to cut "carbon intensity" rather than limit emissions may not satisfy US lawmakers.
After denying the Holocaust again last week, Iran's president threatened to cut off the hands of any aggressors. Recent defiant rhetoric may indicate Tehran is worried about looming international talks on its nuclear program.
The Senate Finance Committee hopes to produce the last of Congress's five draft healthcare bills this week. Then begins the difficult process of melding them together.
At Tuesday's UN meeting, Presidents Obama and Hu set down markers for what they expect to achieve at the December climate change summit in Copenhagen.
A tax expert says Obama's plan could cost some families more money. Whether that is a tax is largely a matter of semantics.
To battle climate change, President Obama told the UN on Tuesday that the US is ready to join other developed countries in cutting emissions.