It’s important to note that this poll was conducted in late May and early June and was published in early July, before Governor Perry announced his entry into the race. For some reason, the results are getting re-posted on various Paul blogs and Facebook sites.
Moreover, look at the column on their methods:
Most importantly, they polled Texas Republican Primary voters, while our sample focused on highly involved Republican voters with clusters in the most politically active Republican areas of the state and using lists taken not only from voter rolls but also from other sources likely to identify voters whose awareness of candidates and issues is substantially higher. Basically, they polled voters and we polled more of the grassroots party activists who will influence those voters.
In other words, rather than choosing likely voters or even Republican Primary voters, they cherry-picked who they polled.
Another blog has this quote from founder Dave Nalle:
“In that poll,” he replied, “It was a mix of precinct chairs, campaign donors, and multiple-repeat voters in Republican primaries. So at the very least they were reliable Republican voters, but a majority of them, about 55%, were actively involved in party organizations, either in clubs or as precinct chairs. I was able to get lists because I have connections within the Texas Republican Party. I was able to get lists from local Republican clubs and from precinct chairs in those parties.”
In contrast, a poll of Republican Primary voters at about the same time showed that Perry would have received 31% of the vote.