Hagel was asked about a White House meeting last week at which 11 Republican members of Congress told Bush his conduct of the war was threatening GOP seats on Capitol Hill.
"The president may find himself standing alone sometime this fall where Republicans will start to move away, and you're starting to see trap doors and exit signs already with a number of Republicans," Hagel said.
He said there is "uneasiness in the Republican Party" over Iraq, and called the GOP delegation that visited Bush "just the tip of the iceberg."
Hagel has talked about running for president in 2008, but has not announced a candidacy. He said Sunday he would decide whether to run by late summer, and hinted at running as an independent.
"I think a credible third ticket, third party would be good for the system," he said. "It would force both parties that have been hijacked by the extremes of their two parties."