The New York Times reported the philosophical quibbling between the White House and House Republicans over the 2013 budget was over and the numbers are close.
The National Association of Home Builders said Tuesday that business confidence among builders had risen modestly in December for the eighth consecutive monthly gain.
By close of trading, the Dow Jones industrial average added 115.57 points, 0.87 percent, to 13,350.96. The Standard and Poor's 500 gained 16.43 points, 1.15 percent, to 1,446.79. The tech-heavy Nasdaq composite added 43.93 points, or 1.46 percent, to 3,054.53.
On the New York Stock Exchange, 2,276 stocks advanced and 816 declined on a volume of 4 billion shares traded.
In Tokyo, the Nikkei 225 index added 136.15 points, 1.37 percent, to 10,059.16.
In London, the FTSE 100 index gained 0.4 percent, 23.75 points, to 5,935.90.
The benchmark 10-year U.S. Treasury note rose 2/32 to yield 1.817 percent.
The dollar rose to 84.38 yen, up from Monday's 83.89 yen. The euro rose to $1.3228 from Monday's $1.3163.