WASHINGTON (CNN) -- For the first time, the Senate is expected to vote Wednesday on a Republican measure that would force President Bush to report to Congress how he intends to revise U.S. strategy if the Iraqi government fails to meet certain benchmarks.

The vote will be largely symbolic but significant because it represents growing Republican frustration about the war.

A top GOP leadership aide described the vote as a "pressure valve" release designed to allow senators to vent their concerns about the lack of progress in Iraq.

"There's a lot of sentiment in our conference that you can't force order and democracy on people who don't want it. It (the lack of progress) is having an impact on us," the GOP aide said.

Sponsored by Sen. John Warner, R-Virginia, and written with the help of several mostly moderate Republicans who have been uneasy about the direction of the war for some time, the measure would require the president to submit two reports to Congress -- one on July 15, 2008 and the other on September 15, 2008. If the reports show "unsatisfactory" progress, President Bush would have to inform the Congress of "revisions to the political, economic, regional, and military components" of his strategy. He would also have to include the "advisability of implementing aspects" of the Iraq Study Group's recommendations and suspend about $3 billion in economic aide to Iraq.

In addition, the measure says the president "shall" remove all U.S. forces if the Iraqi parliament carries through on its threat and passes a resolution directing U.S. troops to leave that country -- something Republican leader Mitch McConnell, R-Kentucky, told CNN Sunday the U.S. would gladly do.

According to McConnell, the Warner amendment is likely to be one of four Iraq votes Democratic leader Harry Reid, D-Nevada, scheduled on an unrelated water resources bill. Reid scheduled the amendments on the water bill so the overdue Iraq war supplemental funding bill can move unencumbered into a conference committee with the House by next week.

Reid said Democrats will offer two amendments -- one which will cut off funding for the war by April of next year and the other which will require troops to leave Iraq unless the Iraqi government makes significant political and security progress but will give the president the right to waive that requirement.

A fourth amendment, offered by the Republicans, will likely mirror President Bush's request for a clean spending bill.