Schmidt was a big financial supporter when Barack Obama was running for president. He's been appointed to the president's council of advisors and now that Google is under investigation by the Federal Trade Commission and the Department of Justice, there are questions about that relationship.
Google acknowledged Friday it's being investigated by the FTC. The FTC is looking into complaints that Google manipulates its search engine results to highlight Google-owned subsidiaries like YouTube while burying the competition.
"There are a huge number of complaints, people, many websites feel that what Google is doing in unfair," UC Berkeley Boalt Hall School of Law Prof. Aaron Edlin, Ph.D., said.
Edlin is an expert on antitrust issues. He says there been a lot of pressure for the government to investigate Google to see if what they are doing is illegal.
"And it may be, though my betting right now is that a case won't be brought," Edlin said.
The government is also investigating Google in connection with online advertising for so-called "rouge pharmacies" that operate outside the law.
In 2010 Google filed a suit against those kids of advertisers saying, "Rogue pharmacies are bad for our users, for legitimate online pharmacies and for the entire e-commerce industry."
Google promised to go after those advertisers.
Consumer Watchdog sent a letter to the White House counsel Friday expressing concern that the president's been entertaining Google executives at the White House while these cases are pending and that poses an inappropriate conflict of interest.
"So the White House shouldn't be embracing a company and its chief executive officers when that company is under criminal investigation by the Justice Department, antitrust investigation by the Federal Trade Commission," Consumer Watchdog President Jamie Court said.
The president does have a close relationship with Google's Executive Chairman Eric Schmidt. When the president came to the Bay Area earlier this year, he invited Schmidt to dinner with other high tech CEO's and Schmidt was at the recent White House state dinner for Germany's chancellor.
"Google needs to be frozen out of these White House state dinners and high profile White House events while it's under criminal investigation and antitrust investigation," Court said.
Google posted a lengthy statement Friday acknowledging the FTC investigation, but the search giant did not respond to ABC7's requests for a statement on the close relationship some Google executives seem to have with the president. Neither did the White House press office.