According to a poll of Israelis this week, three of five respondents disbelieve Olmert's denial and want him to resign. Sensing his vulnerability, senior members of his centrist Kadima party have begun jockeying to succeed him as the party's leader. Several politicians have an eye on replacing him as prime minister.
Foreign Minister Tzipi Livni, Israel's chief negotiator in talks with the Palestinians, is first in line to become prime minister but faces strong rivals within Kadima.
Defense Minister Ehud Barak, another contender, could bring down the government by pulling his left-leaning Labor Party from the governing coalition.
But neither party is eager to force an early election because polls show that opposition leader Benjamin Netanyahu of the Likud party, a right-wing critic of the peace process, is Israel's most popular politician.
By pledging to resign if indicted, Olmert appears to have bought time until police finish collecting evidence and Atty. Gen. Menachem Mazuz decides how to proceed.
That will allow Olmert to promise Bush this week that he will keep working to end the conflict. Olmert said Tuesday that he and Palestinian Authority President Mahmoud Abbas had reached "understandings and points of agreement" on some issues, but he gave no details.
Bush, who is to hold two private meetings with Olmert during a 48-hour visit, told Israeli journalists at the White House that he considers the Israeli leader "an honest guy" but sidestepped questions about his ally's longevity in office.
"It's a legal matter inside the system," Bush said, adding that negotiations to create an independent Palestinian state do not hinge only on Olmert. "This is a plan of a government."
Since Bush launched the latest round in November, the talks have produced few signs of progress on the main issues of borders, the fate of Palestinian refugees and conflicting claims to Jerusalem. Palestinian leaders have criticized Olmert's government for not making enough good-faith gestures, such as removing security checkpoints or halting expansion of settlements in the West Bank.
But Palestinian negotiator Saeb Erekat said Olmert's political demise would make things worse.
"If he's out and they go to early elections," Erekat said, "that means peacemaking is on hold for a year."
How much time Olmert has to make a deal depends on the attorney general.
