Senate Majority Leader Harry Reid, D-Nev., said a budget agreement could be completed before the end of the week.
"If this can be finally passed and signed, it is one more thing off the market's plate," Themis Trading partner Joe Saluzzi told the Wall Street Journal.
The other drama in Washington is the potential for the Fed to announce Wednesday that it has a plan to ease out of its $85 billion per month asset purchasing program that has provided liquidity in financial markets and suppressed interest rates.
An announcement is scheduled for 2 p.m. EST Wednesday.
Stocks on Tuesday dove early, but retrieved lost ground after Reid's remarks on a possible budget deal.
The session ended with the Dow Jones industrial average down 9.31 points, or 0.06 percent, at 15,875.26.
The Standard & Poor's 500 index closed down 5.54 points, 0.31 percent, at 1,781. The Nasdaq composite index lost 5.84 points, 0.14 percent, at 4,023.68.
On the New York Stock Exchange, 3.2 billion shares traded with 1,443 stocks moving higher and 1,657 declining.
The dollar traded higher against the euro at $1.3767, but moved lower to 102.64 against the yen.
In foreign markets, the Nikkei 225 index in Japan added 125.72 points, 0.83 percent, to 15,278.63. The FTSE 100 in Britain lost 36.01 points, 0.55 percent, to 6,486.19.
The 10-year benchmark treasury note rose 10/32 to yield 2.843 percent.
Gold gave up $12.60 on the Comex division of the New York Mercantile Exchange, dropping 1 percent to $1,231.80 per troy ounce. Silver also lost ground, losing 18.1 cents to $19.92, off 0.9 percent.
In late trading, crude oil lost 33 cents to $97.16 per barrel.
On the Chicago Board of Trade, corn for March delivery added 4 cents to $4.2725 per bushel. January delivery soybeans added 6.75 cents to $13.445. March wheat lost 1.75 cents to $6.20.
Notable deaths of 2014 [PHOTOS]