Republican presidential candidates arrive on stage for the GOP debate on Thursday at the Quicken Loans Arena in Cleveland. Getty Images

Whether the candidates' politics or antics were the reason, the first primetime GOP primary debate left many Americans wanting more. Messages wondering when the next debate will be held flooded Twitter minutes after Thursday's event concluded and stretched into Friday morning, by which time more than 4,500 users had tweeted the phrase, according to Topsy analytics. The interest made sense: Early viewership estimates put the debate's audience at about 10 million.

So what's next? In the short term, probably more campaigning. The second GOP primary debate was scheduled for September 16 at the Ronald Reagan Presidential Library in Simi Valley, California. It is sponsored by CNN and Christian broadcasters, the Salem Media Group. Chief CNN Washington correspondent Jake Tapper and radio talk show host Hugh Hewitt were set to moderate.

The participants in the next debate were due to be chosen in a similar manner to Thursday's event. "One grouping will feature the top 10 candidates according to public polling, and the other will include candidates who meet the minimum threshold of 1 percent in public polling but are ranked outside the top 10," CNN reported.

Fox News initially had those same requirements but loosened them to include candidates polling under 1 percent. That lower threshold allowed South Carolina Sen. Lindsey Graham, former New York Gov. George Pataki and former Virginia Gov. Jim Gilmore to participate.

The September debate will be broadcast live on CNN, CNN International, CNN Español and the Salem Radio Network.

After that, the GOP debate schedule was as follows: October 28 in Colorado, December 15 in Nevada, February 6 in New Hampshire, February 13 in South Carolina, and February 26 in Houston. Debates were also expected in Wisconsin in November and in Iowa in January, USA Today reported.

The Democrats were organizing debates October 13 in Nevada, November 14 in Iowa, December 19 in New Hampshire and January 17 in South Carolina. Florida and Wisconsin were due to hold debates on unspecified dates in February and March.