Iowa state Sen. Joni ErnstJoni Kay ErnstKimmel writer tweets amount NRA has given lawmakers in response to shooting prayers Both sides of immigration fight unhappy with Senate debate White House plays defense after FBI testimony MORE (R) has built a big lead over her Senate primary opponents, according to a new automated poll from the Democratic firm Public Policy Polling.

Ernst leads the GOP field with 38 percent support, putting her above the 35 percent of the vote she'll need to win the primary and avoid a party convention.

Meanwhile, wealthy businessman Mark Jacobs (R) has dropped to 18 percent, former radio host Sam Clovis (R) is at 14 percent and former U.S. Attorney Matt Whitaker (R) is at 6 percent.

The state senator has benefitted from some strong ads and Jacobs's failure to catch on, coupled with a ton of outside help, including endorsements from former Alaska Gov. Sarah Palin (R) and former presidential nominee Mitt Romney (R). The big question is whether Jacobs's recent attack ads can slow down her momentum. 

In the general election, 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 (D-Iowa) has maintained his lead over the GOP field.

Braley leads Ernst by 45 percent to 39 percent in the poll, a similar margin as PPP found in February and a sign that his controversial "farmer from Iowa" comments haven't damaged his campaign much at this point. He has slightly larger leads over his other GOP opponents.

The automated phone poll of 914 registered voters with an internet oversample for cellphone users was conducted from May 15-19 and has a margin of error of plus or minus 3.3 percent.