On Tuesday, "Business Insider Today" hosted a Republican presidential primary debate featuring former Gov. Bill Weld of Massachusetts and former Rep. Joe Walsh of Illinois.

Those two candidates, along with former Gov. Mark Sanford of South Carolina, are challenging President Donald Trump for the Republican presidential nomination in 2020.

While Trump declined Business Insider's invitation to participate, and Sanford had a scheduling conflict, Weld and Walsh made their case for their candidacies and discussed the future of the GOP.

Tune into "Business Insider Today" on Facebook or watch a recording of the debate here:

Weld, who announced his campaign in April, was the Republican governor of Massachusetts from 1991 to 1997. He was Gary Johnson's running mate on the Libertarian Party ticket in 2016 but has since switched back to the GOP.

So far, Weld, who is challenging Trump from the center, hasn't been able to generate much buzz for his campaign.

Unlike Weld, Walsh is a staunch ideological conservative. But Walsh is betting on Republican fatigue with Trump's impulsive and dysfunctional governing style, the way he personally demonizes his opponents, and his frequent lies.

Read more: Republican primary voters are annoyed that their party is canceling primaries to benefit Trump

Even though Trump and Walsh are more ideologically similar than Trump and Weld, Walsh's hard-hitting, in-your-face style and near-constant onslaught of criticisms against Trump could damage the president in the general election.

Both Walsh and Weld have gone all in to criticize Trump's behavior and conduct in office. Hours before the debate began, House Democrats announced a formal impeachment inquiry into Trump.

Walsh also told Insider he agreed with several of Trump's other policy positions, including his focus on nominating conservative judges, deregulating private industry, and aligning with the National Rifle Association on gun issues as well as with the administration's decision to move the US Embassy in Israel to Jerusalem.