Evidence of the federal government’s growing influence on Washington area commercial real estate is illustrated in big deals it is working on both sides of the table: auctioning a 127,000-square-foot Bethesda building previously occupied by the National Institutes of Health and moving to snatch up vast spaces in buildings on the private market that have been vacant for months. The General Services Administration is seeking to unload the 10-story building that the NIH vacated in 2002 when it consolidated offices into other buildings in Bethesda. The recommended opening bid for the online auction, which runs from April 30 to July 2, is $14 million. At the same time, federal leasing activity is expanding, according to Jones Lang LaSalle, the real estate firm representing the government. The government signed deals for 750,000 square feet of space in the District in the first quarter of 2010, compared with 670,000 square feet in the city for all of 2009.