Story Highlights• NEW: Sen. Harry Reid asks Bush to present alternative if he vetoes timetable
• Bush reiterates veto vow, says politicians shouldn't dictate how to run war
• General says Iraq, like Northern Ireland, must learn to live with some violence
• Reid, D-Nevada, says Bush's Iraq policy "leads to endless war"
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WASHINGTON (CNN) -- As Democrats ponder their strategy in the face of an inevitable veto of their proposal to withdraw troops from Iraq, President Bush met privately Monday with the top U.S. commander in the war-ravaged nation.
Bush and Gen. David Petraeus discussed the status of the new strategy in Iraq, which both men have recently said is beginning to show signs of success.
"There's been some progress," Bush said during a press briefing after his meeting. "There's been some horrific bombings, of course. There's also been a decline in sectarian violence."
Bush said Petraeus will meet with lawmakers on Capitol Hill later Monday to brief them on "what's going right and what's not going right."
Meanwhile, Senate Majority Leader Harry Reid of Nevada said that Congress will no longer "turn a blind eye to the Bush administration's incompetence and dishonesty." (Watch how Reid has spurred a war of words over Iraq )
He further said that winning the war in Iraq is a political rather than military endeavor.
"Our troops have already done their job. They routed the Iraqi military, captured Baghdad in days, deposed and then captured the dictator. The military mission has long since been accomplished," Reid said during a speech at the Woodrow Wilson International Center for Scholars. "The failure has been political. It has been policy. It has been presidential."
In the Monday briefing, Bush reiterated his vow to veto any timetable to withdraw troops and said, "I believe strongly that politicians in Washington should not be telling generals how to do their job."
"Artificial" deadlines for withdrawing troops serve only to embolden the insurgents and discourage Iraqis and U.S. troops, Bush said.
"I will strongly reject an artificial timetable for withdrawal," Bush said. "No matter how tough it may look, for the Congress to micromanage this process would be a mistake."
Reid defended the Democratic deadline for withdrawing troops, calling it "fair and reasonable."
"If the president disagrees, let him come to us with an alternative," Reid said. "Instead of sending us back to square one with a veto, some tough talk and nothing more, let him come to the table in the spirit of bipartisanship."
In a Friday speech in East Grand Rapids, Michigan, Bush said the two-month-old strategy Petraeus is administering should not be judged until later this year, but that "the operation is meeting expectations."
"There are still horrific attacks in Iraq, such as the bombings in Baghdad on Wednesday, but the direction is beginning to shift," Bush said, referring to a string of at least six bombings last week that killed almost 200 people.
Petraeus told The Washington Post on Sunday that the increase in U.S. and Iraqi troops since February has yielded a more secure Baghdad and Anbar province as well as a lull in sectarian violence.
General tells Post: Iraqis must live with attacks
The improved security situation also has encouraged some markets to reopen and some refugees to return home, he said.
However, Petraeus told the newspaper, bombings like those Wednesday in Baghdad make the ultimate success of the mission uncertain. While they can't be stopped completely, he said, it is reasonable to believe that coalition forces can prevent the insurgent attacks from causing "horrific damage."
"I don't think you're ever going to get rid of all the car bombs," Petraeus told the Post. "Iraq is going to have to learn -- as did, say, Northern Ireland -- to live with some degree of sensational attacks."
Bush has requested that an additional 26,000 troops be sent to Iraq as Democrats have bandied about a proposal to pull U.S. forces out of the country. (Watch the defense secretary explain that the U.S. does not have unlimited patience in Iraq )
The Democratic proposal is tied to a war-funding bill. The House passed legislation last month that would fund the war, but would require all combat operations to cease by September 2008. A softer, nonbinding Senate proposal calls for troops to come home before April 1.
The House and Senate Appropriations committees were expected to reconcile the two bills during a Monday meeting.
The Pentagon has said it can fund the war through June.
Bush said in his Friday speech that the Democrats' deadline is "arbitrary" and that pulling troops out of Iraq would allow al Qaeda to seize control of the nation and allow Iran to exploit the "chaos" that would ensue.
"Withdrawal would embolden enemies and confirm their belief that America is weak and does not have the stomach to do what is necessary to lay the foundations for peace," Bush said. "Ultimately, withdrawal would increase the probability that American troops would have to return to Iraq and confront an enemy that is even more dangerous."
In his Monday response, Reid painted the president's war policy as unilateral and devoid of consideration from his own generals and the Iraq Study Group.
He also echoed the Democratic call for a "new direction" in Iraq.
"One road leads to endless war with consequences for America's future security extending well past the borders of Iraq," Reid said. "The other road leads to a responsible end, gives Iraq the best chance for success and allows us to refocus on the challenges we face throughout the world."
"There's been some horrific bombings, of course. There's also been a decline in sectarian violence," Bush said Monday after meeting with a top general.
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