WASHINGTON (CNN) -- House Democratic leaders are preparing a new version of the Iraq war funding bill that would pay for the war in two stages.

The first stage would give the Bush administration about half of the $95.5 billion it seeks for U.S. troops and military operations. Congress would vote on authorizing the second half of the funds in July, but only after it reviews a report from President Bush on a series of benchmarks measuring the Iraqi government's progress.

The new draft bill, as reported in the Wall Street Journal, was floated by House leaders last week as a way to appeal to the various factions in the House Democratic caucus. A vote on the bill could be scheduled as early as the end of this week.

Leaders hope to move swiftly in order to mesh the House proposal with the Senate's bill before the Memorial Day holiday.

Although this proposal does not include dates for withdrawal, one leadership aide maintains it still demands accountability from Bush because "it doesn't just give him another $100 billion with no questions asked."

The aide said that by "fencing off" the second installment of war funding, Congress would get more detailed information about how the money would be spent and how much more is needed. The aide described the plan as "being responsive to concerns of members who really want us to keep the pressure on Bush, and at the same time we are making sure we are funding the troops and making members comfortable with that."