President Barack Obama said Monday afternoon that a deal was not done, but was "within sight." Senate Minority Leader Mitch McConnell, R-Ky., later said a deal on taxes was done and an overall deal was "very, very close," MarketWatch reported.
Major market indexes rose early, but gains picked up in the afternoon. By the close of trading, the Dow Jones industrial average had gained 1.28 percent or 166.03 points to 13,104.14, closing up 7.3 percent for the year.
The Nasdaq gained 2 percent or 59.20 points to 3,019.51, gaining 16 percent since the first of the year.
The Standard and Poor's 500 added 1.69 percent, 23.76 points, to 1,426.19, a gain of 13 percent in 2012.
On the New York Stock Exchange, 2,642 stocks advanced and 447 declined on a volume of 3.1 billion shares traded.
The 10-year treasury note was off 17/32 to yield 1.761 percent.
The euro fell to $1.3204 from Friday's $1.3217. The dollar rose to 86.73 yen from 85.97 yen.
Markets in Japan were closed for a bank holiday.
In London, the FTSE 100 index shed 0.47 percent, 72.56, to 5,897.81.