SAN FRANCISCO - U.S. stocks closed lower Wednesday, paring losses during the trading session as investors looked for a possible thaw in negotiations over the government shutdown after a private-sector jobs report came out weaker than expected.

SAN FRANCISCO — U.S. stocks closed lower Wednesday, paring losses during the trading session as investors looked for a possible thaw in negotiations over the government shutdown after a private-sector jobs report came out weaker than expected.

The Standard & Poor’s 500 index declined 1.13 points, or 0.1 percent, to finish at 1,693.87.

The Dow Jones industrial average closed down 58.56 points, or 0.4 percent, at 15,133.14, with shares of United Technologies Corp., Coca-Cola Co. and American Express Co. weighing on the index.

The Nasdaq composite finished the day down 2.96 points, or 0.1 percent, at 3,815.02. Earlier in the session, the Nasdaq had been down nearly 30 points.

As the government shutdown dragged into its second day, stocks started to bounce off their intraday lows as President Barack Obama invited congressional leaders to the White House for a late-afternoon meeting to discuss the situation and the looming debt-ceiling crisis.

Investors are “having a little rethink over the implications and longevity of the U.S. government shutdown,” said Andrew Wilkinson, chief economic strategist at Miller Tabak, in emailed comments Wednesday.

Some strategists now say there’s a clear chance the shutdown could blend with the debt-limit debate, prolonging the shutdown to mid-October. They’ve also noted a longer shutdown would create more of a drag on the economy and might call into question Washington’s ability to reach a debt-ceiling deal. The debt-ceiling issue is widely seen as more important.

“I think it’s impossible to handicap how long this is going to take,” said Mark Luschini, chief investment strategist at Janney Montgomery Scott, about the shutdown, which he estimates will drag on GDP by 0.1 percent a week. “In the meantime, the market’s going to be under pressure, but we’re not at a violent selloff yet.”

A huge selloff would be triggered if gridlock in Washington extends past Oct. 177, when the Treasury will have to start “robbing Peter to pay Paul” to meet obligations and some $30 billion in interest payments in November become threatened, Luschini said.

Investors in the past few years have become somewhat less sensitive to drama in Washington, according to Jim Kee, president and chief economist at South Texas Money Management, which has $1.9 billion in assets under management. But he also said that there will be a stronger market reaction if the current shutdown lasts longer than others, noting the median length for a shutdown is three days.

“If we’re still talking about the shutdown in a week or two, that will create a lot of volatility and downward pressure in markets,” Kee said.

On the jobs front, private-sector employers added 166,000 jobs in September, according to Automatic Data Processing Inc. But economists polled by MarketWatch had expected a September gain of 180,000. ADP also reduced August’s gain to 159,000 from 176,000.

“The job market appears to have softened in recent months,” said Mark Zandi, chief economist of Moody’s Analytics, which prepares ADP’s report, in a statement. “Fiscal austerity has begun to take a toll on job creation.”

The ADP report is taking on greater significance this week, because the government’s monthly jobs report might not come out if the shutdown continues.

While Federal Reserve chief Ben Bernanke avoided commenting on monetary policy at a conference sponsored by the St. Louis Fed, Federal Reserve Bank of Boston President Eric Rosengren earlier in the day said that tapering of monthly asset purchases by the central bank could move slowly in the next several years.

In overseas trading, European stocks fell after the European Central Bank left key interest rates unchanged as expected.

Asia markets closed mostly higher, while gold rose and oil futures gained.

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