The Washington Times reported that the Simon campaign has authorized the survey, which will be paid for by the Republican National Committee.
"The president will have access to the poll by the first of next week and will know whether Simon's candidacy is still viable," a source close to the White House and the Simon campaign told the Times. "If not, I expect Bush to walk after Labor Day."
Simon's campaign was stunned last week when a Los Angeles jury found his investment firm guilty of defrauding a former business partner. The jury awarded businessman Paul Edward Hindelang $78.3 million in damages from William E. Simon & Sons and $18.9 million in damages from another investment firm.
Hindelang founded payphone company Pacific Coin, in which Simon & Sons invested in 1998. The lawsuit, which didn't name Simon personally, involved Hindelang's claims that the investors destroyed Pacific Coin by overloading it with debt in a risky secret plan tot take it public.
Simon formed the investment firm in 1998 with his brother and his father, former Nixon Treasury Secretary William E. Simon.
The Times reports that if the president does decide to walk away from the Simon campaign, it will be done quietly, with no announcement. He simply would not personally attempt to raise more money for Simon after Aug. 24, the newspaper said.
"Opinion is split among (Republican) strategists in the state," nonpartisan consultant Allan Hoffenblum told the Times. "But most of the ones I talk to think the president should come out here to raise month for Bill this month."
On Wednesday, Vice President Dick Cheney fulfilled an earlier commitment to raise money for Simon as part of a one-day swing through California, but he did not appear with him in public, nor did he volunteer a word of support for the candidate.
However, the Times reported that Bush had decided to keep his commitment to appear at three Simon fund-raising events in California on Aug.23-24. Those events are expected to raise $3 million.