Senator Juan Hinojosa seeks a two-year moratorium on increases, while Senator Judith Zaffirini wants hikes restricted to 5 percent each year.
The final outcome is in doubt as other members proposed other amendments.
Average fees at the 35 public universities have increased 86 percent since 2003, and are now $6,300 per year.
At the moment, Keshav Rajagopalan is president of UT's Student Government and represents 50,000 students. He says his organization supports Senator Zaffirini's idea.