Rice's comments cast fresh doubt on a potential compromise between the Democratic-led Congress and the White House in getting money to U.S. troops.
Also, with a regional conference on Iraq set to begin Thursday in Egypt, Rice raised the possibility of a rare direct encounter between high-level U.S. and Iranian officials. Foreign Minister Manouchehr Mottaki is expected to lead his country's delegation.
"I would not rule it out," Rice told Bob Schieffer. "We will be there not to talk about U.S.-Iranian issues, but to talk about Iraq, and how Iraq's neighbors can help to stabilize Iraq, and I won't rule it out."
In Washington this week, Bush plans to veto a $124.2 billion war spending bill that includes a timeline for withdrawing U.S. forces from Iraq. In a second version, Democratic leaders may scrap the timetable but work with Republican lawmakers on benchmarks: ordering the Iraqi government to fulfill promises on allocating oil resources, amending its constitution and expanding democratic participation.
Rice said the president would not agree to a plan that penalizes Baghdad if the Iraqi government fall shorts. To do so, she said, would restrain the abilities of Gen. David Petraeus, the top U.S. military commander in Iraq, and Ryan Crocker, the new U.S. ambassador to Iraq.
"Why tie our own hands in using the means that we have to help get the right outcomes in Iraq?" Rice said. "That's the problem with having so-called consequences for missing the benchmarks."
Rice said that the Iraqi government is not moving forward fast enough, but "General Petraeus and Ambassador Crocker have a plan and a way forward."
Benchmarks have emerged as a possible rallying point as U.S. leaders seek to show they are holding the Iraq government accountable. But establishing goals without consequences may seem pointless to many Democratic lawmakers, who want an aggressive change in policy.
"The benchmarks — the Iraqis agreed to it, the president agreed it," said Democratic Rep. John Murtha, who also appeared on Face The Nation. "We're saying to them, well, let's put some teeth into the benchmarks."
Rice said it makes sense to give Iraq's leaders time to meet the goals they have set. She said Bush has made clear to Prime Minister Nouri al-Maliki that people in the United States have limited patience.
In their push to link U.S. money or troop support to Iraqi performance, however, Democrats must negotiate with Republicans. On their own, Democratic lawmakers do not have the votes to override Bush's veto.
Bush is expected the veto the existing war bill by Tuesday, then meet Wednesday with congressional leaders on the next steps.
"If he vetoes this bill, he's cut off the money, but obviously, we're going to pass another bill," Murtha said. "I'd like to see two months ... Fund it for two months instead of a year. And then look at it again."
Meanwhile, Rice said will not appear in person before the House Oversight and Government Reform Committee to answer questions about the Bush administration's prewar intelligence. Rice said she already has addressed claims that Iraq had sought uranium from the African nation of Niger.
The committee voted 21-10 last week to issue a subpoena to compel her testimony.
Asked about the possibility of being held in contempt by the committee chairman, Democratic Rep. Henry Waxman, Rice said, "That's the chairman's prerogative. I respect the oversight — the oversight responsibilities of Congress — but I frankly think this one has been looked at and looked at and looked at."