According to one interpretation in this report, that’s part of the message that King Abdullah meant to send with his harsh criticism of the war:

With regard to Iraq, the Saudis seem to be paying some attention to internal American politics. The Senate on Tuesday signaled support for legislation calling for a timeline for withdrawal from Iraq in exchange for further funding for the war.
Last November, officials here realized that a Democratic upset could spell major changes for the Middle East: a possible pullout from Iraq, fueling further instability and, more important, allowing Iran to extend its influence in the region.
“I don’t think that the Saudi government has decided to distance itself from Bush just yet,” said Adel alToraifi, a columnist here with close ties to the Saudi government. “But I also think that the Saudis have seen that the ball is moving into the court of the Democrats, and they want to extend their hand to Speaker of the House Nancy Pelosi.”