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Stocks Close Up 1% on 'Cliff' Talks; Apple Jumps 3%

Stocks closed higher for the second session Tuesday, with major averages hitting a two-month high, as investors were encouraged that a deal would soon be made in Washington to avoid the "fiscal cliff."

Stocks briefly came off their highs after Senate Majority Leader Harry Reid said House Republicans are threatening to abandon negotiations, but soon regained their footing.

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The Dow Jones Industrial Average jumped 115.57 points, or 0.87 percent, to end at 13,350.96, led by Bank of America and United Technologies.

The S&P 500 climbed 16.43 points, or 1.15 percent, to close at 1,446.79. The Nasdaq rallied 43.93 points, or 1.46 percent, to finish at 3,054.53. The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, ended below 16.

Most key S&P sectors ended in positive territory, led by energy and techs.

In the latest budget talks, House Speaker John Boehner proposed a "Plan B" option to extend the Bush-era tax cut for people making less than $1 million on Jan. 1, but deferring a plan on spending cuts.

"I continue to have hope that we can reach a broader agreement with the White House," said Boehner in a press conference. "But at this point, having a back up plan to make sure that as few taxpayers are affected by this increase as possible is the right course of action for us." (Read More: 'Cliff' Talks Holding Markets Hostage)

But the White House rejected Boehner's "Plan B" option, saying the approach wouldn't pass the Senate and that the President won't accept a deal that doesn't ask enough of the wealthy.

Hopes for a deal grew on Monday after President Barack Obama made a counter-offer to Republicans that included a major change in position on tax hikes for the wealthy. Obama is looking for $1.2 trillion in higher tax revenue from those earning more than $400,000, and would implement $1.22 trillion in spending cuts, including to some social programs, according to reports. (Read More: US 'Fiscal Cliff' Deal Closer, but a Divide Remains)

"You have an agreement in principal and we're just working on the details—it's inching forward and sounds like things are getting closer," said John Fox, co-manager of the FAM Value Fund. "The market's seeing a good December already and if we see some resolution, the rally will certainly continue."

Meanwhile, ratings agency Standard & Poor's lifted Greece's sovereign credit rating to "B-minus" with a stable outlook, citing its European partners' efforts to keep the country part of the euro.

Financials gained after widely-followed bank analyst Meredith Whitney turned bullish the sector. Whitney also upgraded Bank of America, Citigroup and Discover Financial to "buy" from "hold."

Apple rallied after the iPhone maker was reiterated with an "outperform" rating at Cowen. Separately, rival Samsung says it will withdraw European injunction requests against Apple.

Knight Capital rallied as the company is getting closer to a sale. The market maker is expected to enter into exclusive talks with either Getco or Virtu Financial on the sale of the company, according to sources.

Arbitron surged after Nielsen said it will acquire the radio station ratings provider in a deal worth $1.26 billion.

Oracle is scheduled to post earnings after the closing bell.

On the economic front, home builder sentiment index climbed for an eighth-straight month, according to the National Association of Home Builders. Homebuilders including Beazer, Pulte and Toll Brothers rallied.

"Housing is definitely getting better, as a lot of the indicators have shown," said Fox. "Homebuilders have also reported forward orders, which have been going up for a number of months."

The U.S. current account deficit fell more than expected in the third quarter to $107.5 billion, the lowest in nearly two years, according to the Commerce Department.

Treasury prices remained lower after the government auctioned $35 billion in 5-year notes at a high yield of 0.769 percent. The bid-to-cover was 2.72.

—By CNBC's JeeYeon Park (Follow JeeYeon on Twitter: @JeeYeonParkCNBC)

Coming Up This Week:

WEDNESDAY: MBA mortgage apps, housing starts, oil inventories, 7-yr note auction; Earnings from FedEx, General Mills, Accenture, Bed Bath & Beyond
THURSDAY: GDP, jobless claims, corporate profits, existing home sales, Philadelphia Fed survey, FHFA home price index, leading indicators, Fed balance sheet/money supply, UPS busiest day; Earnings froM CarMax, ConAgra, Darden Restaurants, Discover Financial, Rite Aid, Nike, RIMM, Micron
FRIDAY: Quadruple witching, personal income & outlays, Chicago Fed activity index, consumer sentiment, BLS state employment stats; Earnings from Walgreen

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