(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window.) * Futures up: Dow and S&P 0.6%, Nasdaq 0.7% March 3 (Reuters) - U.S. stock index futures rose on Wednesday as a swift global roll out of vaccines and a new round of stimulus bolstered bets on a quick economic rebound, with investors also focusing on private employment and service sector reports. Texas sweepingly rolled back coronavirus restrictions on Tuesday, lifting a mask mandate and saying most businesses may open at full capacity next week as many U.S. states record a sharp decline in new infections and hospitalization. President Joe Biden also said the United States will have enough COVID-19 vaccine for every American adult by the end of May. The U.S. Senate is expected to take up Biden’s $1.9 trillion coronavirus relief package on Wednesday, with Democrats aiming to get it signed into law before March 14, when some current jobless benefits expire. At 06:35 a.m. EST, Dow E-minis were up 202 points, or 0.64% and S&P 500 E-minis were up 21.5 points, or 0.56%. Nasdaq 100 E-minis were up 86.5 points, or 0.65%. Futures tracking the small-cap Russell 2000 jumped about 1.1%. Further aiding risk sentiment, the U.S. 10-year Treasury yield was last up 1.44%, well below last week’s peak of above 1.61% that triggered a selloff in the equities market on valuation worries. Investors have lately unwound positions in high-flying technology-focused stocks and moved into sectors that are likely to benefit from an economy recovery, including financials , energy and industrials. Bank of America, Goldman Sachs and Morgan Stanley were up between 1.2% and 1.7% in trading before the bell. ISM’s survey is expected to show U.S. services industry activity remained at its highest level in nearly two years in February, unchanged from January. A separate report is likely to show U.S. private payrolls rebounded further in February after the economy shed jobs in December. It comes ahead of the more comprehensive monthly jobs report. Chevron Corp and Exxon Mobil Corp rose about 1.5% each as oil prices were boosted by expectations that OPEC+ producers might decide against increasing output when they meet this week. However, Exxon said that it planned to cut its workforce in Singapore, home to its largest oil refining and petrochemical complex, by about 7% due to “unprecedented market conditions” resulting from the COVID-19 pandemic. (Reporting by Shashank Nayar and Medha Singh in Bengaluru; Editing by Anil D’Silva)