Five states hold primaries in big tests for Trump

• Backing Greitens, as Trump was rumored to be considering, would have risked adding a high-profile loss to Trump's ledger. Polls have showed Schmitt leading the primary field, with Greitens falling to third place in recent weeks.
• Publicly, Schmitt and Greitens each claimed Trump’s backing and said they were honored.

Why it matters The success or failure of Trump-backed candidates — in both primaries and the general election — is an important barometer of his long-term grip on the party.

Arizona Republicans are poised to nominate a roster of MAGA-aligned candidates.

• A Trump sweep in Arizona, one of the most important battleground states, would be an embarrassing rebuke to Gov. Doug Ducey and former Vice President Mike Pence, who spent valuable political capital against several of Trump's candidates.
• But that could actually hurt their prospects of defeating Sen. Mark Kelly (D-Ariz.) or holding the governor's office.

Details: Most public polling has shown Trump-endorsed former TV anchor Kari Lake with late momentum against Pence-endorsed businesswoman Karrin Taylor Robson in the Arizona governor's race.

• Lake has been badly outspent but boasts considerable grassroots support.
• Trump's slate of downballot candidates — including Blake Masters for the Senate, Mark Finchem for secretary of state and Abe Hamadeh for state attorney general — are favored in their respective primaries. All have sowed doubt about President Biden's 2020 election victory.
• Arizona House Speaker Rusty Bowers, who testified to the Jan. 6 committee about Trump's efforts to overturn the Arizona election, is expected to lose a state Senate primary to a challenger promoting Trump's election conspiracy theories. Bowers told ABC's Jon Karl it would take a "miracle" for him to win.

In other pivotal primaries, Trump's favored candidates have struggled to gain political traction.

• In Washington state, Reps. Jaime Herrera Beutler and Dan Newhouse, both of whom backed Trump's impeachment, have a solid chance at defeating insurgent challengers.
• Michigan Rep. Peter Meijer, who backed Trump's impeachment, is in more precarious shape. Democrats spent $435,000 in his primary to boost his Trump-endorsed challenger John Gibbs. Anticipating a defeat, Meijer slammed Democrats for bankrolling his challenger's underfunded campaign.

Squad goals: Tuesday's contests also include a number of key battles in an ongoing struggle between progressives and more moderate, establishment Democrats -- which, as Axios reported Sunday, progressives have been mostly losing.

• Two members of the Squad — Reps. Rashida Tlaib (D-Mich.) and Rep. Cori Bush (D-Mo.) — are facing moderate primary challengers tonight, along with a third, Ilhan Omar (D-Minn.), on Aug. 9. All are favored to win re-nomination.
• Moderate Rep. Haley Stevens is facing progressive Rep. Andy Levin in a primary that has become a proxy battle among Democrats over support for Israel. Stevens, who's supported by pro-Israel groups, has surged ahead in independent polling.

Kansas voters will vote in on an amendment to the state constitution on abortion restrictions — the first in a series of ballot measures on abortion in the wake of the Supreme Court's June decision overturning Roe v. Wade.

• Kansas, despite its conservative politics, currently protects abortion rights in the state Constitution, allowing the procedure up to 22 weeks into pregnancy.
• If the amendment passes, however, it would allow state legislators to restrict or ban abortions.

Editor's note: This story was corrected to make clear that Rep. Ilhan Omar's primary will be held Aug. 9. An earlier version of the story suggested it would be held tonight.