WASHINGTON —  With President Bush's speech to outline his new policy in Iraq scheduled for Wednesday night, the new Democrat-led Congress is hungry to show it too can wield power on Iraq policy despite the bulk of military and foreign policy authority resting in the executive branch.

Bush is expected to say in his prime-time address that he will send at least another 20,000 troops to Iraq — what is being labeled a troop "surge" — as well as place political benchmarks on the Iraqi government in an effort to stem sectarian violence that is tearing apart the country.

Sen. Edward Kennedy is expected on Tuesday to outline his plans for a bill that would cut money from troop "escalation" in a speech in Washington. That would follow similar discussions in recent days by other prominent Democrats.

"The Congress has the power of the purse and what we are saying is: Before the president sends additional American troops into the civil war, the president has to come back to the Congress and get the authority for that deployment," Kennedy told NBC's "Today" show on Tuesday.

"We ought to take this step and stop the surge," Kennedy said.

Democrats on Capitol Hill are seeking answers to key questions, including: Can Congress put conditions on upcoming spending proposals that will parse out costs associated with the surge from ongoing operations? Can they make payments for the war conditional on political milestones Iraqis are being asked to reach?

Bush submits his annual budget next month, which the White House says will include funding for Iraq and Afghanistan. But Congress is likely to get an emergency supplemental spending request to cover the $100 billion more that the Pentagon says it needs to finance military operations in Iraq and Afghanistan through the end of the fiscal year that ends Sept. 30.

"My office is now investigating what tools are available to us to condition or constrain appropriations," Sen. Barack Obama, D-Ill., a member of the Senate Foreign Relations Committee said Monday, adding, "I'm not willing to create a situation in which troops already in Iraq might be shortchanged in some way because of restrictions on appropriations."

House Speaker Nancy Pelosi on Monday didn't back down from comments she made over the weekend saying the president's proposals will be watched closely.

"We're all hopeful that the president will make a proposal that we can all work together on. But the president needs to know — and that's what I was telling him yesterday — is that congressional oversight is alive and well in the Congress of the United States," Pelosi, D-Calif., said.

"If the president is proposing an escalation, we want to see a justification for the mission," she said. "I think you will see a supplemental subjected to some pretty harsh scrutiny."

Sen. Russ Feingold, D-Wis., who is an ardent Iraq war opponent, told FOX News he believed lawmakers can find ways to carve money out of the budget separate for the surge. He acknowledged it would be difficult.

"This surge has to be stopped. It's a reckless, mindless approach to a desperately difficult situation, so we have to look at all options," Feingold said.

The lawmakers' comments contrasted with remarks by Sen. Joe Biden, D-Del., one day earlier on NBC's "Meet the Press." Asked about what can be done about the military situation in Iraq, Biden said, "There's not much I can do about it — not much anybody can do about it. [Bush] is commander in chief."

"If he surges another 20, 30 [thousand], or whatever number he's going to, into Baghdad, it'll be a tragic mistake, in my view, but, as a practical matter, there's no way to say, 'Mr. President, stop,'" said Biden, chairman of the Senate Foreign Relations committee.

In a separate appearance, Senate Minority Leader Mitch McConnell, R-Ky., also said Congress is limited.

"We could pass resolutions, we can have hearings, we can debate the matter, which we will do. But I don't think Congress will have the ability to simply micromanage the tactics in the war, nor should it," he said on "FOX News Sunday."

Distinguishing himself again from several members in his own party, Sen. Joe Lieberman, D-Conn., on Monday continued to show his support of the war, calling it a "mistake" to not increase funding should the president ask for more troops.

"Because I support an increase in American troops in Iraq to bring that country the security it needs to achieve the political settlement that's the ultimate answer, I would oppose any attempt here in Congress to cut off funding for the additional troops that I hope President Bush recommends later this week. I think that would be a profound mistake," Lieberman said.

Lieberman was joined by Sen. Lindsay Graham, R-S.C., in sending a letter to Bush on Monday urging him to increase the number of troops in Iraq. Graham said plenty of mistakes have been made in Iraq but those opposing troop increases or calling for withdrawals must offer an alternative, and suggested any of those proposals would likely lead to chaos in Iraq and the broader Middle East.

"I think it would be a monumental mistake that we would pay for for decades. If the Congress of the United States tries to micromanage this war, it would be a shift in responsibility under our Constitution that would be of a longstanding nature," Graham said, adding that attempts by Congress to control troop levels would run afoul of ground-level military leadership.

But not all Republicans are tripping over themselves to kill discussion about reducing or withholding war funds.

Sen. Gordon Smith, R-Ore., attended a White House meeting Monday on Iraq and said he would be open to hearing out the details of placing conditions on the emergency war spending proposal that is expected from the White House by the end of January.

Smith told FOX News he was skeptical of withholding money, calling it "dishonorable to take away the bullets" from soldiers on the battlefield. But in regard to implementing such an option on Iraq operations, he said, "Whether we're there yet is an open question."

One Republican senator with extensive experience in the appropriations process told FOX News said methods are available to limit the amount of money for the war effort, but Democrats likely would not want to risk being seen not supporting the troops.

"Congress can do anything it wants in the appropriations process. They can write in conditions however they want," said the senator, who asked not to be identified by name because of the sensitivity of the subject.

The senator said a specific "reconstruction fund," for instance, could be made available only if Iraqis met goals such as a Sunni-Shiite oil revenue-sharing agreement.

FOX News' Trish Turner contributed to this report.