But behind the scenes, the experience - while positive in demonstrating audience demand for such coverage - did highlight some issues with the current set-up, and a need for the non-profit news outlet to invest in its own technology.
As it happens, the video and audio was made available via a feed from the Texas State Capitol. The Texas Tribune picked up the feed, and made it "scalable and streamable" by sharing it on YouTube with the world, Rodney Gibbs, chief innovation officer at the Tribune, told Journalism.co.uk.
In comparison, the Texas Capital's feed is limited to its online player, which carries viewing restrictions, or a selection of broadcasters in the local area, Gibbs said.
But while the Tribune helped spread the reach of the video using YouTube, the news outlet was still not in control of what was shown.
This meant, that when the official session closed at midnight, so did the feed. But in reality, events, such as the protests surrounding the debate, continued well into the early hours. The Tribune was not in control of where the camera was pointing, or the audio - and this is what they want to change.
On Friday last week (27 September), the Tribune launched a Kickstarter campaign to crowdfund $60,000 "to make unfiltered video the norm in politics". At the time of writing it was $15,000 into the campaign.
The livestreaming experience so far
From January to August this year the Texas Tribune was sharing live video from "every minute of the 83rd Texas legislature", Gibbs told Journalism.co.uk. "All the floor debates, everything that happened on the floor of the Senate or the House, we livestreamed on our site."
While it was not all necessarily the most captivating viewing for a general audience, the video was capturing an audience of between 500 to 1000 on average, and "we were glad to do it", Gibbs said.
And the abortion bill debate, which was the scene for the 11-hour filibuster by Wendy Davis, saw viewing of the video rocket to around 200,000 viewers across the world. "It just went nuts," Gibbs said.
"That certainly did a lot to change our thinking about livestreaming, about the impact you can have, about the immediacy. Over 100 other sites and TV stations were streaming our stream - they picked it up and embedded it on their sites.
"So that got us very excited about this. I think it also set the expectation in our audience that this is the new norm."
Later today, Gibbs said that Davis is expected to announce that she is putting herself forward as a candidate for Texas governor, and that some Tribune readers are assuming it will be livestreamed.
"Because it went so well last time people assume it's the norm now," he explained. "Which is what prompted us to start this Kickstarter campaign because we do want it to be the norm.
"We don't think every story merits a livestream, a lot of it doesn't, but for things like this that are breaking news or big events, it's good to have that tool in your toolbelt."
While Tribune reporters have previously broadcast live video using mobile devices, "the quality is quite poor and the reliability is poor", Gibbs said, "because you're trying to stream it over a cell network and using a consumer-grade device".
This coverage is often used, therefore, "to augment or as colour to our primary reporting", instead of it being the main event of the coverage.
How the crowdfunded investment will be used
The Tribune wants to use the funding to invest in "satellite backpacks", which will work by connecting to a camera and then using "multiple cell networks", as opposed to a single network a mobile would use. This will enable the reporter to produce "a high definition image", Gibbs explained.
"So someone could be with the crowd, or in the press area, or chasing someone down the street with this backpack, and still be broadcasting a broadcast-quality, high-definition video signal."
The plan is to then "livestream a full year of intense 2014 election coverage".
"We already have the crackerjack reporting and data teams covering the candidates, the issues, the campaigns, the finances, the debates – everything, in other words," the Kickstarter campaign page says. "We just don't have the ability to livestream it."
The Tribune also announced on Tuesday (2 October) that it will offer a free livestreaming webinar to help others produce similar work, if the campaign is successful.