WASHINGTON (Reuters) - Republican Donald Trump’s list of potential vice presidential running mates got a little shorter on Wednesday when one prominent U.S. senator withdrew from consideration and a second said she wanted to focus on her home state. The moves by Bob Corker of Tennessee and Joni Ernst of Iowa could complicate Trump’s efforts to rally establishment Republicans behind his presidential bid. With Trump looking at a self-imposed deadline of July 15 to announce his pick, there was no indication that the wealthy businessman was anywhere close to reaching what is perhaps the most important decision he will make as the presumptive Republican nominee. Trump is looking to announce his running mate just ahead of the Republican National Convention, to be held July 18-21  in Cleveland, where he is expected to become the party’s official nominee. In Cincinnati, Ohio, on Wednesday, Trump campaigned with potential vice presidential candidate Newt Gingrich, a former speaker of the House of Representatives who is popular in conservative circles. Introducing Trump, Gingrich tried out the role of the No. 2 with a robust attack on presumptive Democratic nominee Hillary Clinton for her email practices, on the same day the Justice Department decided not to levy criminal charges over what the Federal Bureau of Investigation called her “extremely careless” handling of classified information when she was secretary of state. “There are two Americas. There’s the corrupt Washington of the old order. And there’s all the rest of us. I say to you, Enough!” Gingrich said. Trump liked what he heard. “I’m not saying it’s Newt, but if it’s Newt, nobody is going to be beating him in those debates,” Trump said.  Trump told Fox News he has 10 candidates on his vice presidential list, including two generals. One source said Indiana Governor Mike Pence is being pushed internally by some members of Trump’s inner circle. A former congressman, Pence met with Trump on Saturday. Corker, from Tennessee, who is chairman of the Senate Foreign Relations Committee, had wrestled privately over whether to be a contender for the No. 2 position, telling friends he had never been a surrogate for another politician. Corker spent eight hours at Trump Tower in New York on Tuesday, then campaigned with Trump in Raleigh, North Carolina. He told reporters he withdrew because “I just felt like I was far more suited for other types of service.” “You know, it’s a highly political role for the next four months,” he said. “I view myself as deep in substance and policy, and I just think there are better ways for me to serve in the public arena.” His withdrawal eliminates an important party establishment figure as Trump tries to broaden his appeal with plans to visit Republicans in the Senate and House on Capitol Hill on Thursday. “Corker’s withdrawal could be considered a canary in the coal mine with establishment Republicans who are convinced that Trump cannot stay on message and can’t stay focused on attacking Hillary Clinton without doing some type of damage to his campaign,” said Republican strategist Ron Bonjean. Some Republicans felt Trump erred by not taking full political advantage of FBI Director James Comey’s statement on Tuesday that Clinton mishandled classified emails. In Raleigh, Trump sharply attacked Clinton but strayed from the message by saying the late Iraqi leader Saddam Hussein had done a good job cracking down on militants. Ernst, a rising figure in the Republican Party, spent part of the Fourth of July holiday on Monday meeting with Trump. She seemed to be leaning against the vice presidential position, and told Politico, “I made that very clear to him that I’m focused on Iowa. I feel that I have a lot more to do in the United States Senate. And Iowa is where my heart is.” 