WASHINGTON (CNN) -- It's one of the biggest arguments the Iraq war's supporters use to condemn critics in Congress. And, if Democrats have their way, it may be replaced.

Democratic senators are talking Monday about revising the authorization for use of force in Iraq that was passed by Congress in 2002. They would do so by working to pass a new resolution putting additional restrictions on military action in the country.

Senate Democratic leaders have tentatively agreed to try to modify the 2002 resolution, two senior Democratic aides told CNN.

On Sunday's political talk shows, Democrats chatted up the idea. "I've been working with some of my colleagues to try to convince them that that's the way to go -- to repeal and restate the president's authority, make it clear that the purpose that he has troops in there is to, in fact, protect against al Qaeda gaining chunks of territory, training the Iraqi forces, force protection, and for our forces," Sen. Joe Biden, a presidential hopeful, told CBS's "Face the Nation."

"We can have a much more limited mission that we authorize," Sen. Carl Levin, D-Michigan, told Fox News Sunday.

Sen. Hillary Clinton, who has made a promise to end the Iraq war part of her presidential campaign, meanwhile announced her own idea. Clinton is one of many Democrats calling for "phased redeployment" to steadily remove many U.S. troops from Iraq. "It's time to say that redeployment should start in 90 days, or the Congress will revoke authorization for this war," she says in the latest video posted on her campaign Web site.

It's unclear whether Democrats could muster the 60 votes necessary to even hold a vote on a resolution. They tried, but failed Saturday to hold a vote on a non-binding resolution condemning President Bush's plan to send 21,500 more U.S. troops to Iraq. The House passed such a resolution Friday.

"The next resolution will force the president to change the strategy," Sen. Chuck Schumer, D-New York, vowed Monday on CNN's "American Morning." He said he believes more Republicans will steadily join the Democrats in working to pressure the president "because his strategy is misguided."

While some Republicans in both chambers of Congress have joined Democrats in opposing the president's Iraq policy, others support him. A vote on a new Iraq war authorization would be a "huge mistake, in my view, when we are just beginning to execute a new strategy," Sen. Jon Kyl, R-Arizona, told CNN.