Even as he rakes in millions of dollars for his campaign war chest from Wall Street types, Mitt Romney seems to have left two titans of industry with a skeptical impression of how he is running his campaign for the White House.

First it was Rupert Murdoch, the chief executive of News Corp., who tweeted Sunday that Romney’s GOP presidential campaign team was insular and outmatched by President Obama’s.

“Met Romney last week. Tough O Chicago pros will be hard to beat unless he drops old friends from team and hires some real pros. Doubtful.”

Romney, who is vacationing in New Hampshire, is standing by his team, which includes a mix of longtime aides, such as Eric Fehrnstrom and Beth Meyers, who is heading the search for Romney’s vice presidential nominee.

“Gov. Romney respects Rupert Murdoch and also respects his team and has confidence in them” said Romney press secretary Andrea Saul.

Murdoch’s grumblings, which Jack Welch, the former chief executive of General Electric, echoed later in a no-room-for-amateurs tweet of his own, seem to stem from conversations that he had with Romney last week in New York.

Hope Mitt Romney is listening to Murdoch advice ont campaign staff..playing in league with Chicago pols..No room for amateurs

— Jack Welch (@jack_welch) July 2, 2012

According to someone who attended the meeting but wanted to only speak on background, Murdoch pressed Romney and his aides to get tougher on Obama. Murdoch later tweeted about that issue and his concerns about the Latino vote.

In response to a Twitter follower who said that Romney had brains but needed more stomach and heart, Murdoch tweeted:

“Romney has all these and more, but just to see more fight. And Hispanics a surrender to O. Cn not afford, hurts senate too.”

Polls show that Romney is lagging badly among Latino voters. According to a person who attended the meeting, Romney insisted that he would maintain his position on immigration rather than risk appearing to switch sides. He also touted Sen. Marco Rubio (R-Fla.) as a top surrogate who would help him attract support among Latinos.

Despite his series of gaffes during the Republican primary, Romney is even with Obama in most polls and has pulled ahead of the president in raising cash.

On Monday, Fehrnstrom sided with Democrats who have said that the Massachusetts health care plan put in place under Romney penalized people who didn’t buy insurance, rather than levied a tax. Republicans have used the tax argument — part of Supreme Court ruling that upheld the law — to try to reframe the health care debate and tag Democrats as tax-and-spend liberals. Fehrnstrom’s comments seemed to take that issue off the table.

Murdoch later tweeted: “Romney people upset at me! Of course I want him to win, save us from socialism, etc but should listen to good advice and get stuck in!”