Thirty-five percent of respondents said they would vote for a write-in candidate, a statistical tie with the 36 percent support for Democrat Nick Lampson, according to the poll of likely voters in the Houston area's 22nd Congressional District.
Of the respondents who said they'd choose a write-in candidate, 79 percent said they planned to name Shelley Sekula-Gibbs, a Houston city councilwoman backed by the Republican Party.
Twenty-five percent of surveyed voters said they were still undecided.
"Both candidates seem to be swimming upstream here," said pollster John Zogby, president of Zogby International, which conducted the poll. "What's clear on one hand, is Nick Lampson seems to have had the opportunity and has not closed the deal just yet. On the same token, Shelley Sekula-Gibbs has a great opportunity in a Republican district."
The poll was conducted for the Houston Chronicle and KHOU-TV and appeared on their Web sites Sunday night.
The poll also shows that 62 percent of respondents were aware that there's a write-in candidate. Sixty-one percent said they know how to cast a write-in vote.
Two lesser-known candidates are running as write-ins along with Sekula-Gibbs.
Four percent of respondents said they would vote for Libertarian Bob Smither, the only person besides Lampson on the general election ballot.
Fifty-two percent of poll respondents identified themselves as Republicans, 32 percent as Democrats and 16 percent as independent.
"Punditry was coloring the district blue. It's still a Republican district. Even harder than selling a write-in, is selling a Democrat in this district," Zogby said.
DeLay, the former House majority leader, resigned from Congress in June amid legal and ethical problems. He had already won the GOP nomination for his district. But the courts refused to allow Republicans to replace him on the ballot, forcing them to turn to a write-in candidate.
Sekula-Gibbs said the poll results show that Lampson is a weak candidate.
"I think we are at the top of the hill. We are ready to plant the flag," she said.
Lampson, who served in the U.S. House from 1997 to 2004, said it's hard to predict how many people will vote for a write-in candidate.
"I felt this was doable from the beginning and I still feel that way now," Lampson said. "I knew I had to reach out to a community used to voting one way politically. And I've had to ask those people to have confidence in me."
Zogby International conducted the telephone survey of 504 likely voters between Oct. 23 and Oct. 25. It has a margin of error of plus or minus 4.5 percentage points.