Republican presidential candidate Mitt Romney holds a safe lead in the U.S. state of Texas, with a support rate of 58 percent against President Barack Obama's 39 percent, a new poll released Tuesday shows.

The non-partisan Texas Lyceum Poll finds that among likely voters, 58 percent would vote for Romney and Paul Ryan. Thirty- nine percent would vote for Obama and Vice President Joe Biden.

Republican Ted Cruz also leads Democrat Paul Sadler by 24 points on the U.S. Senate ballot, according to the poll which was conducted September 10-26.

When asked about the direction the country is headed, 42 percent of the surveyed believe that the country is moving in the right direction, while 51 percent believe that they are off on the wrong track.

Looking at personal economic evaluations, equal proportions of the surveyed said they were better and worse off than they were a year ago, both at 24 percent, while 50 percent said that they were doing about the same.