Schultz said in a Wednesday-morning tweet that he plans to run for reelection as secretary of State instead.

"I am humbled by all of the encouragement to run for Senate, but I love serving Iowans as Secretary of State... I intend to run for SOS," he tweeted.

Reps. Tom Latham and Steve King, as well as Lt. Gov. Kim Reynolds and state Agriculture Secretary Bill Northey have all decided against a run as well.

Of the remaining possible contenders, none are well-known by Iowans. According to a Quinnipiac poll released earlier this month, only 8 percent of respondents feel favorably about the only announced GOP contender, former U.S. Attorney Matt Whitaker, while 86 percent say they don't know enough about him.

David Young, former chief of staff to Sen. Chuck GrassleyCharles (Chuck) Ernest GrassleyThe Hill's Morning Report — Trump’s walk-back fails to stem outrage on Putin meeting Senate GOP poised to break record on Trump's court picks This week: GOP mulls vote on ‘abolish ICE’ legislation MORE (R-Iowa), is likely to jump in the race, but 94 percent of respondents haven't heard of him.

And former Iowa GOP Chairman AJ Spiker is also considering a run, but 91 percent of those polled said they hadn't heard of him. State Sen. Joni Ernst and businessman Ron Langston could also enter the race.

Some Republicans have expressed concern that the likely primary will weaken their eventual candidate, while the likely Democratic nominee, Rep. Bruce BraleyBruce Lowell BraleyOPINION | Tax reform, not Trump-McConnell feuds, will make 2018 a win for GOP Ten years later, House Dems reunite and look forward Trump: Ernst wanted 'more seasoning' before entertaining VP offer MORE — the only Democrat to announce his intentions for the seat — cruises through the primary unchallenged and amasses a strong war chest for the general.