A new poll in Texas shows Gov. Rick Perry (R) starts out with a big lead in his 2014 primary, but that just more than a quarter of Texas voters say they will definitely support him in the general election.

Texas Gov. Rick Perry (R) (Richard Shiro/Associated Press)

The University of Texas/Texas Tribune poll shows 26 percent of Texans support Perry no matter who he faces, 36 percent would vote against him and 33 percent want to see who else runs.

That's pretty dangerous territory for an incumbent.

There is also some thought that Perry could face a primary challenge from state Attorney General Greg Abbott (R) — though Perry has said Abbott has assured him that won't happen.

While Perry enjoys a solid 72 percent approval rating among Republicans, just 48 percent say they plan to vote for him in the primary. In a head-to-head match-up with Abbott, Perry leads 49 percent to 17 percent — owing plenty to Perry's superior name ID.

The poll was conducted online, which is not generally regarded as the most accurate method of polling. But they mirror the results of a recent automated poll from Democratic firm Public Policy Polling, which found that 31 percent of Texans thought Perry should seek reelection, while 62 percent said he should step aside.

Perry made a big splash in his 2010 primary by easily dispatching then-Sen. Kay Bailey Hutchison (R-Tex.), but he has never been overwhelmingly popular in his home state. He won in 2010 with 55 percent of the vote, despite it being a very good year for Republicans, and he took 39 percent in a four-way race in 2006.

Perry is considered safer than his numbers suggest, though, given the dearth of top Democratic recruits. Despite Texas trending toward being a competitive state, Democrats have been unable to field top-tier candidates for statewide offices.

In related news, one of the third-party candidates in that 2006 race, Kinky Friedman, said over the weekend that he is looking at another run. Friedman, a satirist known for his quips and quirks, took 13 percent as an independent candidate.

In saying he was considering another campaign, Friedman offered this: "I’m gonna be cremated and I want my ashes spread on Rick Perry’s hair.”

Perry has been in office since President George W. Bush ascended to the presidency after the 2000 election and is leaning toward a run for a fourth full term.

He has also made clear that he may run for president again in 2016, despite what is regarded as a pretty disastrous 2012 effort.