"It's amazing how this market absorbs bad news since the Bear Stearns debacle; people just want to own stocks," said Dave Rovelli, managing director of equity trading at brokerage Canaccord Adams Inc.
After struggling in positive territory at the start, the Dow Jones Industrial Average was more recently off 34.44 points to 12,591.59.
The S&P 500 declined 1.73 points to 1,367.58, while the Nasdaq Composite shed 3.12 points to 2,360.18.
An hour ahead of the opening bell, stock index futures shaved strong gains after the Labor Department said U.S. employers cut back their hiring in March for the third month in a row, with the unemployment rate soaring to 5.1%, the highest since September 2005. .
On the New York Mercantile Exchange, crude-oil futures gained, with the spot month up $1.16 at $104.99 a barrel. .
Gold futures edged lower, with the contract for June delivery off $2.6 to $907.3 an ounce. .
In overseas trade, stocks in Tokyo fell, with automobile shares among those weighting on the market. .
In Europe, shares wobbled in the wake of the U.S. jobs data. .
By Kate Gibson