By Richard Cowan

WASHINGTON (Reuters) - Democratic leaders in the House of Representatives have agreed on a plan to fund the Iraq war into next year but included a provision to withdraw combat troops by the end of 2009, lawmakers said on Tuesday.

The plan for supporting the approximately $170 billion request from President George W. Bush to fight wars in Iraq and Afghanistan also would expand education benefits for war veterans and give more help to the long-term U.S. unemployed.

House Appropriations Committee Chairman David Obey, a Wisconsin Democrat who is an outspoken opponent of the Iraq war, said the legislation would give Bush all the new money he requested for combat "so that whoever becomes president will have a few months to get his or her act together before they submit their plans to extricate us from Iraq."

A new president will be sworn in next January. Democratic candidates Hillary Clinton and Barack Obama have promised to start withdrawing troops if they are elected. Sen. John McCain, who will likely be the Republican nominee, has talked about a possibly long U.S. combat presence in Iraq.

The measure could face problems in the Senate and is expected to be resisted by Bush. He rejects any Iraq withdrawal timetable and opposes the Democrats' plan for expanding veterans' education benefits and extending U.S. jobless benefits for up to six months.

Obey acknowledged that while Democrats can pass troop withdrawal timetables through the House, there was not enough support in Congress overall to win passage.

He said when the legislation reaches the House floor, lawmakers will have a chance to vote on a plan to begin immediate combat troop withdrawals from Iraq with the goal of completing the pullout by the end of 2009.

The full House could vote on Thursday on the plan, which would provide war funds for the remainder of this fiscal year and the next one, which starts on October 1.