Dewhurst was the only one who named specifics, saying lawmakers are looking at lowering business and property taxes. But Perry and Straus also suggested that tax relief was on the horizon.
"I think we have a record proving that tax relief should be a priority, the details of that and the potential for that are yet to be determined," Straus said.
The three leaders appeared together at a Capitol new conference on the second day of the 140-day session after having breakfast at the Texas Governor's Mansion.
Perry, the longest-serving governor in Texas history by far, said he wanted to hear from Texans about what taxes they want to cut before deciding on a plan.
The leaders were far less committal on the level of spending for public education, which was cut by more than $5 billion last session.
Asked if the Legislature would restore funding for public education, Perry suggested that the question itself was flawed. He said education spending has been more than adequate over the last decade.
"We've had public education funding growing at three times the public education enrollment. So you've had a 70 percent increase of funding from 2002 to 2012. You've had a 23 percent increase in enrollment growth," he said. "I think under any scenario over the last decade, the funding that we have seen in the state of Texas for public education has been pretty phenomenal."
"I'm not sure there's any state in the nation that's had that type of [growth], certainly not any big state.," Perry continued. "We're getting the job done in public education."
Straus, who has spoken of the need to build infrastructure for future generations, referred obliquely to "unfinished business" from last session but didn't commit to any specific level of education funding.
Dewhurst said that with school finance litigation pending, the discussion was largely academic.
"We're going to be putting more resources into public education, and there is no reason for us to get into a dialogue back and forth what that number should be because we've got 400, 40 percent of our school districts, have sued us," Dewhurst said. "So we're going to have a court, one or more courts, tell us what is the right number for us to put in and we'll fund it."
Texas Tribune donors or members may be quoted or mentioned in our stories, or may be the subject of them. For a complete list of contributors, click here.