The move comes despite a new poll from Greenberg Quinlan Rosner Research, a Democratic firm, that found a majority of Texans — 51 percent — opposed a proposal that "would put in place new restrictions and regulations on abortion providers that would likely result in the closure of all but five abortion clinics in the state of Texas, all of which are located along the I-35 corridor, and would ban most abortions starting at 20 weeks of pregnancy." Of those surveyed, 42 percent said they support the proposal.

The poll also found that respondents largely opposed using special sessions to pass new abortion legislation. Some eight in 10 Texas voters agreed that "a special session of the legislature should focus on issues like education, jobs, and the economy, instead of bringing up social issues like abortion that were already addressed in the regular session of the legislature."

The liberal survey is a break from other recent polls of the state, including a Texas Tribune poll that found that 62 percent of Texas residents favored banning abortion after 20 weeks.

Davis told MSNBC on Tuesday night that she was appreciative of the supporters who turned out to testify at the committee hearing.

“Thousands of people showed up at the Capitol today to testify and to observe the testimony. I expect that we’ll see that same sort of turnout when the bill is heard in Senate committee hearing, which is going to take place on Monday morning, is my understanding,” Davis said. “And we expect or hope that their voices will add in a way that makes a difference in the way some of these lawmakers are considering this bill.”

This post was updated at 11:40 a.m.