WASHINGTON - Nearly four years after invading Iraq, President Bush is sorting through an array of options - none of them easy - for a way out, including a partial withdrawal of U.S. troops from violence-plagued cities and a redeployment near Iraq's borders with Iran and Syria, his top security aide said Sunday.

Bush is open to several previously rejected possibilities because he realizes “things are not proceeding well enough or fast enough in Iraq,” national security adviser Stephen Hadley told ABC News' “This Week.” “We have to make some changes.”

Hadley said the president is considering a “laundry list of ideas” from a Nov. 6 memo by Secretary of Defense Donald Rumsfeld, who announced his resignation two days later - just after Republicans lost control of the House and Senate in the mid-term elections. The options include the redeployment of substantial U.S. forces to areas near the Iranian and Syrian borders, withdrawing U.S. troops from especially vulnerable positions, and starting modest drawdowns of American forces to encourage Iraqis “to pull up their socks, step up and take responsibility for their country,” Rumsfeld wrote.

“Of course they're being considered,” Hadley said of the suggestions. Iraqi Prime Minister Nuri al-Maliki, he said, “made very clear to the president that he and his unity government want to take more responsibility.”

That's what we've been seeking for three years.”

“They're not there yet,” he added. “They don't have all the tools that they need.”

The Rumsfeld memo suggests that in the days leading to the Nov. 7 election, the administration was torn between staying on course in Iraq or considering options it repeatedly had rejected. Three days before Rumsfeld wrote the memo, Vice President Dick Cheney said in an interview that the administration would continue “full speed ahead” with its policy in Iraq, regardless of the election's outcome. Even if the policy proved unpopular,“ Cheney said, ”it doesn't matter, in the sense that we have to continue what we think is right.“

Rumsfeld's resignation Nov. 8 was widely seen as a nod to voter anger over the war and discontent within GOP ranks.

Hadley said Bush will weigh recommendations from Rumsfeld, congressional Democrats and Republicans, military leaders, Iraqi officials and a soon-to-be-published report by the bipartisan Iraq Study Group. “He is going to then take all of those things and come together with a way forward,” Hadley said on NBC's “Meet the Press.” “His hope is that it is a way forward that the American people can support.”

Some senior Democratic senators, who will be in the majority when the 110th Congress convenes next month, said Sunday that the administration continues to move too slowly in pressing Iraqis to assume control of their nation's security and future.

“I'd do the opposite of what the president did a month ago, when he picked up the phone and called Prime Minister al-Maliki and said, don't worry, we're staying,” Sen. Evan Bayh, D-Ind., who is considering a presidential bid, told ABC. “I'd pick up the phone and say, `You know what, we're not staying forever. You need to start getting your act together.”'

Sen. Joseph Biden, D-Del., another possible presidential candidate and incoming chairman of the Senate Foreign Relations Committee, told Fox News Sunday that the Rumsfeld memo shows “there was a clear disconnect between what the administration has been saying the last year and what's been going on on the ground.” He said no one, including Rumsfeld, “thought the policy the president continues to pursue makes any sense.”

Sen. Carl Levin, D-Mich., who will chair the Senate Armed Services Committee, told NBC that Bush is “not capable of admitting mistakes.” Levin said the United States should begin withdrawing its troops in four to six months. “I know the president has rejected that,” he said. “He's rejected everything that reflects on his policy or that suggests that his policy is wrong or that we've got to change course.”

Republican Sen. Lindsey Graham (S.C.) took a different tack, saying the United States should send more troops to Iraq to quell the sectarian violence and stabilize the nation. He said Bush “needs to tell the American public a failed state in Iraq is a dramatic loss in the war on terror.... We must stay, fight and win in Iraq. I reject timetables” for troop withdrawals.

“And any strategy that unites the country and we lose, I'm against,” Graham told Fox News Sunday. “I'd rather be divided as a nation and win than united and lose.”