DALLAS (CBSDFW.COM) – The Commission on Presidential Debates said Wednesday it’s considering changes to the two remaining presidential debates following Tuesday night’s match-up.

In a statement, the commission said it wants to have a more orderly discussion on the issues.

Minutes into the first debate, the interruptions and insults flew between President Donald Trump and former Vice President Joe Biden.

At one point while the President spoke over Biden, the former Vice President said, “Will you shut up, man?”

During another point in the debate, the President told Mr. Biden, “Don’t ever use that word with me, there’s nothing smart about you Joe.”

The former Vice President called the President a “clown” and said he was the worst President.

President Trump told Biden he accomplished more in 47 months than the former Vice President accomplished in his 47 years in politics.

In this photo illustration the US President Donald Trump and Democratic presidential candidate and former US Vice President Joe Biden are seen during the first presidential debate on a YouTube video displayed on a screen of a smartphone. (Photo Illustration by Pavlo Conchar/SOPA Images/LightRocket via Getty Images)

On Wednesday, supporters of each candidate blamed the other for the bitter back and forth.

Lt. Governor Dan Patrick, the Chair of the President’s re-election campaign in Texas said, “Yeah, it was feisty. You know, from the Trump side, that’s who we elected. Trump is feisty. I thought Joe Biden was nasty and saying things like shut up and calling the president united states a clown. I thought was very disrespectful.”

Texas Democratic Party Chair Gilberto Hinojosa said the former Vice President showed great restraint.

“Anytime you push somebody that repeatedly that ugly for so long, at some point, you have to react. And I think that, you know, a lot of people that were watching, we’re glad that he finally told him to shut up right and, and glad that he finally pointed out to the American people that he was acting like a clown.”

Ben Voth, Director of Debate at SMU described the debate this way: “It was definitely a mess, especially for the first half hour.”

Voth said one idea being discussed may be blunt, but prevent constant interruptions: shutting a candidate’s microphone when it’s not their turn to speak.

Turn on the mic for the time you want them to talk, turn it off, when you don’t want them to talk, then it’s very mechanical. That would begin to move it back to an actual debate.”

He said one trend he’s noticed is that gradually, moderators have been taking up more speaking time during the debates.

Voth said it’s more than 20% now, compared to 5% in 2008.

To change that, he said the moderators could give the candidates a chance to talk about topics without interruptions at first.

“There’s not I don’t think a great need to set up the questions or try to catch the candidates, like what you said, you know, five things in the past. Let me confront you, though. Let the opposing candidate do that if they want to do that. But just a topic, response, topic response. I think that could improve things a lot.”

After Tuesday night, some people have said the remaining two debates should be cancelled.

But both the Lt. Governor and Texas Democratic Party Chair agreed the debates should go forward.