"There has been, for the last six years, a Republican-dominated Congress that has not exercised its prerogative constitutionally and had hearings on Iraq; had hearings on the Medicare program, it isn't working as well as it should; education; on what's going on with health care in this country, generally," Sen. Reid, D-Nevada, told Bob Schieffer.
Reid, who is the Senate Minority Leader in the current lame-duck Congress, promised that the Democrats will not tie up the White House by using the majority party's subpoena power.
He said Democrats will work with the president and the Republicans to look toward the future.
"I think the time has come," Reid said, "with the new elections having been completed, and a whole precedent, that we show the American people that we can govern."
White House Chief of Staff Joshua Bolten, who also appeared on Face The Nation said he was encouraged by the "bipartisan tone that's been coming from" the Democratic leadership.
Both Reid and Rep. Nacy Pelosi, who will become the Speaker of the House in January, have met with Mr. Bush since the Democrats grabbed a majority in both houses of Congress on Election Day.
"You know, it's a big disappointment for us in the White House to have lost control of both houses," Bolten said. But "sometimes in adversity there's opportunity, and hopefully we can take advantage of this opportunity."
The conciliatory tone coming from both sides of the aisle is a dramatic change from the months of fierce campaigning that led up to Election Day.
Democratic candidates across the country attacked their Republican opponents for supporting Mr. Bush's Iraq policies and for the scandals that have plagued the Capitol. The Republican candidates fired back that, if elected, the Democrats would prematurely pull U.S. troops out of Iraq and raise taxes as well.
On Nov. 7, the American people supported the Democratic positions – as the Democrats picked up six seats in the Senate, 28 seats in the House and six governors' mansions.
On Sunday, Reid said his party will not "cut and run" from Iraq or raise taxes – news that relieved the White House Chief of Staff.
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"What do we need to do?" Reid asked rhetorically. "We need to have a re-deployment in Iraq... Pull everybody out now? Of course not."
"I'm encouraged by that," Bolten said later on the show. "The president obviously wants to take a whole fresh look at what we're doing in Iraq. Nobody's happy with what our situation in Iraq is now."
Reid laid out three steps of the Democrat's plan for Iraq. He said the mission needs to change to counterinsurgency, the reconstruction effort needs to be "revitalized" and the president needs to involve Iraq's neighbors for a regional solution.
"Nobody wants to get the troops out of there more than President Bush, but they need to be there to support the Iraqi government, to make sure that the Iraqi government succeeds," Bolten said. If the U.S. leaves behind a failed state, he said it would be "a much worse situation which would be a dangerous haven for terrorists, not just to us, but to the whole neighborhood."
Schieffer asked Reid directly if he planned to raise taxes.
"The answer is no," Reid said. "But it is inevitable, as far as I'm concerned, that this country stop spending red ink."
Reid said the next Congress will have to control spending to get the federal budget back in line. "If you want to have a new program, figure out a way to pay for it without raising taxes," he said.
Bolten said the Republicans need to go back to "some first principles," which sound a lot like what the Democrats are promising when the new Congress begins.
Those principles "are a robust national security, limited government, fiscal responsibility, and moving forward on some of the priorities of the country, like immigration reform, energy independence," Bolten said.