By Susan Cornwell WASHINGTON, April 25 (Reuters) - House Democrats predicted on Wednesday they would win passage of a hotly contested bill that aims to bring U.S. combat troops out of Iraq early next year and which President George W. Bush has said he will veto. "Yes, it'll pass," Rep. Steny Hoyer, the leader of the Democratic majority, said as he entered an 11th-hour session set up by the White House for the U.S. commander in Iraq to persuade lawmakers to give Bush's war strategy another chance. Gen. David Petraeus briefed lawmakers behind closed doors just hours before the full House (of Representatives) was to vote on the bill, which would continue funding the unpopular war but also include an exit timeline which Bush rejects. Democratic Rep. James Moran of Virginia, asked what he wanted to hear from Petraeus, said, "The truth would be something novel." Voting could be close on the House bill, which would set a non-binding March 31 goal for bringing U.S. combat troops out of Iraq. The Senate is expected to pass the bill on Thursday. It provides an additional $100 billion this year for the wars in Iraq and Afghanistan. Bush has railed for weeks against the withdrawal plan attached by Democrats. Republicans said they hoped Democrats would listen to Petraeus, who is leading a strategy in which tens of thousands of extra U.S. and Iraqi troops have been deployed in Baghdad since February to try to staunch the sectarian killing and insurgent attacks. Many doubted Petraeus could change minds after a week in which verbal clashes hardened attitudes. "What he (Petraeus) is talking about is what he's doing on the ground. What Congress is doing, is politics. He is not going to change that," said Sen. Norm Coleman, a Minnesota Republican who visited Iraq last weekend. Bush spokeswoman Dana Perino repeated Bush's charge that Democrats want to set a "surrender date" in Iraq. "The tension is high because the stakes are high. We feel very strongly that leaving before the job is done is turning over the victory to the enemy," Perino said. At least 85 U.S. troops have been killed in Iraq this month, making April the deadliest since December, when 112 were killed. More than 3,300 U.S. soldiers have been killed since the 2003 invasion that toppled Saddam Hussein. But Republicans said the continuing violence should not determine the U.S. approach. "Are we going to let suicide bombers and car bombers define the foreign policy of the United States?" asked Sen. Lindsey Graham, a South Carolina Republican. (Additional reporting by Matt Spetalnick and Donna Smith)