Perino said U.S. advisers began to doubt the deadline months ago, as a corruption scandal and related political uncertainties occupied Israel's attention.
Israeli Prime Minister Ehud Olmert is being forced from office by the scandal, and the country is set to hold new elections in February. Rice noted the situation "is a constraint on the ability of any government to conclude" a deal.
"I've learned never to predict in this business," she said, "but it is clear we're in a different situation now because Israel is going to elections."
En route to the Middle East for her eighth trip to Israel and the Palestinian territories since the parties set the deadline for reaching an agreement at last November's summit at Annapolis, Md., Rice said political uncertainty in Israel is the main obstacle.
Rice also said upon arriving here that it is important to maintain momentum and support for the negotiations so that new governments in both Israel and the United States have "a firm foundation" to continue the talks next year.
"It is our expectation that the Annapolis process has laid groundwork which should make possible the establishment of a Palestinian state when the political circumstances permit," Rice added. "I think that whatever happens by the end of the year, you've got a firm foundation for quickly moving this forward to conclusion."
The two sides for months have been backing away from the timeline pushed in Annapolis.
Although Rice refused to rule out the chance of an agreement by year's end, her remarks reflect the first time that a Bush administration official has publicly not held out hope that the deadline could be met.
"We'll see where they are at the end of the year," said Rice, vowing to "work on this with the parties until the day that we leave."
With her time in office rapidly waning, Rice is hoping to shore up the fragile Israeli-Palestinian negotiations and leave a viable process for the incoming administration of President-elect Barack Obama.
She will also visit Egypt and Jordan to shore up Arab support for the talks. At some point before Obama moves into the White House on Jan. 20, Rice said she would like to see the sides memorialize the progress they have made but not stretch to conclude a partial deal.
"It will be important to wrap up all of that work one way or another," she said.
Separately, Foreign Minister Tzipi Livni, discussing handing over the peace process to the Obama administration and the new administration to be elected early next year in Israel, said that "it is important that we preserve the process within the structure that we have created."
"We are realistic enough to recognize the reality we face, but we are also determined enough to change it. I believe deeply that stagnation is not in Israel's interest and cannot be our policy," she said.
Rice, when questioned about whether the U.S. was looking for a document of some kind to lay down on paper what progress the sides have made and whether they have reaffirmed their commitment to the Annapolis agreement, replied: "As I understand it, they are going to affirm that the Annapolis process and the framework it establishes is indeed the basis on which they believe they can come to a resolution of their conflict, regardless of anyone's timetables."
Livni also said that President-elect Barack Obama shouldn't talk to Iran just yet, warning that such dialogue could project "weakness" - a first sign of disagreement with the incoming American administration.
Obama has stated a willingness to talk to Iran about its nuclear program, which Israel, the U.S. and others believe is aimed at developing an atomic bomb. His policy marks a departure from that of the Bush administration, which has refused to engage Iranian leaders.
Iranian President Mahmoud Ahmadinejad congratulated Obama on Thursday, the first time an Iranian leader has offered such wishes to a U.S. president-elect since the 1979 Islamic Revolution. Ahmadinejad sent a message to Obama in which he congratulated the Democrat on "attracting the majority of voters in the election."
The text of the note was carried by the official IRNA news agency.
Associated Press writer Karin Laub in Jerusalem and White House Correspondent Jennifer Loven in Washington contributed to this report.