* Payrolls much higher than forecast, unemployment rate matches lowest since Sept 2008
* Futures up: Dow 33 pts, S&P 5 pts, Nasdaq 13 pts (Updates prices, adds data, comment)
By Rodrigo Campos
NEW YORK, July 3 (Reuters) - U.S. stocks were set to rise at the open on Thursday after the unemployment rate fell to its lowest in almost six years and the American economy created many more jobs than forecast.
The U.S. economy created 288,000 jobs in June and the unemployment rate declined to 6.1 percent, the lowest since September 2008.
The data confirmed expectations that the economy bounced back in the second quarter after a dismal start to the year, and will likely spark talk about the need for the Federal Reserve to normalize monetary policy sooner rather than later.
Futures added to small gains when the payrolls data was published, but quickly pared those advances and were briefly negative. The Dow and S&P 500 closed at record highs Wednesday and face psychological round-number barriers.
The payrolls data "is obviously very strong across the board," said Michael O'Rourke, chief market strategist at JonesTrading in Greenwich, Connecticut.
"We're at record highs and it is telling that equities are having a little trouble with this number. That could indicate worries that the Fed is behind the curve, and that it shouldn't be on autopilot with respect to tapering. Maybe they should be doing it faster."
S&P 500 e-mini futures were up 5 points and fair value - a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract - indicated a slightly higher open. Dow Jones industrial average e-mini futures rose 33 points and Nasdaq 100 e-mini futures added 13 points.
The Dow is 24 points away from 17,000 while the S&P has 2,000 in sight.
The closing bell will ring at 1 p.m. (1700 GMT) and U.S. markets will be closed Friday for the Independence Day holiday.
Volkswagen denied planning a bid for U.S. truck maker Paccar after analysts published comments in a research note from a senior executive of German rival Daimler saying he had heard of such a plan. Paccar shares were up 4 percent in early trading.
Lululemon shares rose 3.7 percent in light premarket trading as founder Dennis Wilson's advisers have been talking to private equity firms about a possible buyout, the Wall Street Journal reported, citing people familiar with the matter.
Regado Biosciences shares fell 53 percent after the Data Safety Monitoring Board started an unplanned review of data from a trial and the company said patient enrollment has been paused until the DSMB returns with recommendations.
Activist hedge fund Jana Partners LLC reported a 9.9 percent stake in PetSmart and said it planned to ask the company to explore a sale, sending shares of the pet products retailer up 16.6 percent in premarket trading.
(Reporting by Rodrigo Campos, additional reporting by Ryan Vlastelica; Editing by Meredith Mazzilli)