BY JONATHAN CHENG

Hopes that lawmakers in Washington will reach an agreement on taxes and spending gave investors new confidence and drove stock indexes to their best day in two months.

Investors have spent a tense few weeks since the election watching for smoke signals out of the nation's capital for indications that Democrats and Republicans are nearing a compromise. On Monday, they found reason for optimism.

President Barack Obama said he was "confident" an accord could be reached with lawmakers, and congressional leaders have said they are making progress.

New data Monday also showed existing home sales climbed last month and builder confidence rose to the highest level in 6½ years.

For investors, the stakes are high. If no deal comes to pass by the year-end deadline, a raft of tax hikes and spending cuts would automatically come into effect, potentially dragging the U.S. economy into recession. As big a worry: the wrangling until then could send markets on a wild ride.

"Until we get much closer to a deal, we're going to see more volatility in the markets," said Russ Koesterich, chief investment strategist at BlackRock Inc. "We're going to be hostage to these utterances out of D.C."

Investors and analysts cautioned the gains could quickly be erased should progress in Washington stall, or if new weakness emerges in Europe. Late Monday, Moody's Investors Service stripped France of its triple-A rating, citing its weak economy.

"As a money manager, you don't know where the bottom of the market is, but I don't want to miss the boat if the market goes higher from here," said Reed Choate, a portfolio manager at Neville, Rodie & Shaw, a New York firm with $1.2 billion under management. Mr. Choate said he bought beaten-up stocks of utilities, industrial and energy companies.

After four straight losing weeks, the Dow Jones Industrial Average rose 207.65 points, or 1.65%, to 12795.96, its biggest gain in two months. The Nasdaq Composite rose 2.2%, driven by a 7.2% surge in Apple Inc. AAPL -0.86% Asian markets rose early Tuesday.

A version of this article appeared November 20, 2012, on page A1 in the U.S. edition of The Wall Street Journal, with the headline: Investors Show Optimism That Cliff Will Be Avoided.