If the Republican primary runoff for governor of Texas were held today, incumbent Rick Perry would be a solid favorite, according to a Public Policy Polling (PPP) survey released Tuesday.

But that’s not exactly the good news Perry wants to hear: He’d rather win the nomination outright in the March 2 first-round primary voting and avoid a six-week runoff campaign, but the same PPP poll suggests that’s a bit of a long shot.

To avoid a six-week campaign for an April 13 runoff, Perry would need to achieve a majority vote March 2. And PPP’s sample of 400 Republicans deemed likely primary voters, collected Feb. 19-21, showed Perry with 40 percent support.

That still put him well ahead of the 31 percent for Sen. Kay Bailey Hutchison , his top rival throughout the campaign, and 20 percent for upstart candidate Debra Medina, a businesswoman and county Republican chairwoman with ties to both the conservative activist “tea party” movement and the libertarian conservative philosophy espoused by Texas Rep. Ron Paul . Undecided respondents were 9 percent of the total.

But Perry topped the magic 50 percent threshold in the potential runoff matchups, leading Hutchison by 52 percent to 35 percent with 13 percent undecided and leading Medina by 55 percent to 36 percent with 9 percent undecided.

The poll’s statistical margin of error is plus or minus 4.9 percentage points.

Perry’s drive for 50 percent-plus appears to be hindered by Medina, a states’ rights and gun owners’ rights advocate who is running to the right of both establishment candidates. Perry is already the longest-tenured governor in Texas history, having moved up from lieutenant governor to governor in 2000 when predecessor George W. Bush won for president. He relied strongly on a conservative Republican base in GOP-leaning Texas to win full four-year terms in 2002 and 2006.

Most recent polls had shown Medina in the upper teens, so the 20 percent she received in the poll suggests her own support base does not appear diminished by a recent controversy. That erupted Feb. 11 when Medina, answering a question about “9/11 Truthers” asked by conservative commentator Glenn Beck on his radio show, did not clearly reject the idea that the federal government might have had some involvement in allowing the Sept. 11, 2001, terrorist attacks. Medina the same day said she had been blindsided by the question and stated that she believes terrorists alone were responsible.

The flap, though, may have limited Medina’s growth potential. PPP’s analysis showed her approval vs. disapproval ratings had slipped from 40 percent positive and 9 percent negative in a poll taken about two weeks earlier to 36 percent favorable and 30 percent unfavorable in the more recent poll.

But the new poll also cast doubt on Hutchison’s ability to gain traction in the campaign’s final days. Once widely seen as having strong potential to unseat Perry because of her history of strong Senate job approval ratings, Hutchison’s primary challenge has damaged her popularity among Republicans.

The PPP showed 47 percent approved and 43 percent disapproved of her job performance. Just 24 percent said they wanted her to be governor, which, strangely, is a lower number than said they would vote for her in the primary. Meanwhile, 37 percent said they want her to stay a senator — and 31 percent say they want her out of office altogether.

Perry, seeking to build upon the anti-Washington sentiment voiced these days by most conservative Republicans, has portrayed Hutchison — a senator since 1993 — as part of the problem.

And though Hutchison has gone all out to emphasize her conservative credentials during the campaign, she is widely viewed as the most moderate, or the least hard-line conservative, of the GOP candidates, in part because she has a rather soft-spoken and genteel manner, and in part because she has opposed overturning the Supreme Court’s 1973 Roe v. Wade ruling that legalized abortion (although she strongly contends that her overall record is anti-abortion).