NEW YORK — Optimism that President Barack Obama and Congressional leaders will reach a deal on the budget deficit and avoid the “fiscal cliff” helped stocks notch their first advance in four days.

The market started lower Friday but spiked higher shortly before midday as the top members of the House and Senate spoke at the White House following a closed-door session with Obama. House Speaker John Boehner and Senate Minority Leader Mitch McConnell both said they offered higher tax revenue as part of a deal. Boehner said he outlined a framework that is consistent with Obama’s call for a “balanced” approach of both higher revenue and spending cuts.

“It’s a good start ... the fact that they were all standing together,” said Ben Schwartz, the chief market strategist at Lightspeed Financial, a New York-based broker.

The Dow Jones industrial average closed up 45.93 points, or 0.4 percent, at 12,588.31, after falling as much as 71 points at mid-morning. The Standard & Poor’s 500 index rose 6.55 points, or 0.5 percent, to 1,359.88 and the Nasdaq rose 16.19 points, or 0.6 percent to 2,853.13.