Failure to avoid the cliff could push the country into a recession next year.
At the close of U.S. trading, the Dow Jones Industrial Average finished up 0.87%, the S&P 500 index was up 1.15%, while the Nasdaq Composite index rose 1.46%.
Stocks gained on talk the White House and Congress are closer to agreeing on a plan to push through fiscal reforms and avoid recession next year.
At the end of 2012, the Bush-era tax breaks and other benefits are set to expire at the same time cuts to government spending are scheduled to kick in, a combination known as a fiscal cliff that could contract the economy by 0.5% next year if Congress fails to avoid it, according to Congressional Budget Office estimates.
Both sides of the U.S. political aisle have previously disagreed over the role income tax reforms should play when it comes to crafting a 2013 fiscal framework, with Democrats originally calling for tax hikes on those earning at least USD250,000 a year, with Republicans originally opposed to tax hikes for anyone.
The two political parties have since made concessions, with Republicans warming up to tax hikes on the wealthy by offering to raise rates on those earning a minimum USD1 million a year, with Democrats reportedly countering by raising the floor to USD400,000 from USD250,000.
Sticking points still remain, as Republicans have said they want to see more details surrounding Democratic proposals to cut spending and reform entitlement programs such as Social Security or Medicare, though stocks rallied on optimism that both sides remain willing to work together to find a solution.
Elsewhere, the U.S. current account deficit narrowed in the third quarter of 2012, posting the smallest deficit since the fourth quarter of 2010, government data revealed earlier Tuesday.
The U.S. Bureau of Economic Analysis reported earlier that the country’s current account deficit narrowed to a seasonally adjusted USD107.5 billion in the third quarter from a revised deficit of USD118.1 billion.
Analysts had expected the U.S. current account deficit to narrow to USD103.4 billion in the third quarter.
Leading Dow Jones Industrial Average performers included Bank of America, up 3.27%, United Technologies, up 2.80%, and Hewlett-Packard, up 2.25%.
The Dow Jones Industrial Average's worst performers included General Electric, down 1.09%, Coca-Cola, down 0.59%, and Verizon Communications, down 0.57%.
European indices, meanwhile, finished higher.
After the close of European trade, the EURO STOXX 50 rose 0.59%, France's CAC 40 rose 0.29%, while Germany's DAX 30 finished up 0.64%. Meanwhile, in the U.K. the FTSE 100 gained 0.40%.
On Wednesday, the U.S. is to publish government data on building permits, an excellent gauge of future construction activity, as well as data on housing starts.
The country is also to release official data on crude oil stockpiles.