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* S&P 500 inches towards all-time intraday high
* Data on U.S. private employment, services sector on tap
* Vodafone ADRs fall as Verizon rules out takeover
* Futures up: Dow 16 pts, S&P 2.3 pts, Nasdaq 4.25 pts
By Ryan Vlastelica
NEW YORK, April 3 (Reuters) - U.S. stock index futures rose on Wednesday, putting the S&P 500 even closer to its all-time intraday high as investors awaited the latest round of economic data.
* The S&P has been within striking distance of its record level of 1,576.09 for the past several sessions, edging within three points on Tuesday before pulling back. While the index did end at a new closing high, the fact that stocks pared gains late in the session gave investors a reason to question the strength of the recent rally.
* Moves may be slight until the release of the closely watched nonfarm payrolls report on Friday as there are few major catalysts before then. The S&P is up less than 0.1 percent so far this week.
* Nonetheless, economic data will be scoured for signs on whether the economy continues to steadily improve. The March read for the Institute for Supply Management's services index, due at 10 a.m., is seen coming in at 55.8, down from 56.0 in the previous month.
* The ADP national employment report is scheduled for release at 8:15 (1215 GMT) and is seen showing 200,000 private sector jobs were added in March, slightly more than the previous month. If the ADP report is strong, it may raise expectations for the jobs report on Friday.
* While data has largely been positive, helping to fuel strong gains in the first quarter, there have been some disappointments that have investors cautious. The ISM manufacturing index on Monday came in below expectations.
* S&P 500 futures rose 2.3 points and were above fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures added 16 points and Nasdaq 100 futures rose 4.25 points.
* The S&P 500 is up more than 10 percent so far this year, gains that took it above its 2007 closing high last Thursday, while the Dow first broke above its 2007 record on March 5.
* In company news, Verizon Communications Inc ruled out a full takeover of Vodafone , turning the focus yet again to whether the two telecom giants can do a deal over their Verizon Wireless joint venture.
* U.S.-listed shares of Vodafone fell 3.6 percent to $28.36 in premarket trading.
* Thermo Fisher Scientific Inc is emerging as the lead contender in an auction for Life Technologies Corp , a genetic testing maker with a market value of more than $11 billion, three people familiar with the matter said this week.
* Issues in the euro zone will continue to be in focus a day after Cyprus concluded a bailout deal. The plan, which still requires ratification, would mean the country receives a 10 billion euro loan and that it has until 2018 to carry out measures to shore up its finances. The country's finance minister resigned after concluding the deal.
* While investors have largely used any market decline as a buying opportunity, the situation in Cyprus has been a major source of market uncertainty in recent weeks.
* U.S. stocks rose on Tuesday, lifted by healthcare stocks after a government decision on payment rates. Strong factory orders data also added to the positive tone.