If there is any Senate race that is testing the Democrats’ conviction that they can counter the structural disadvantages they face by focusing relentlessly on pocketbook issues like the minimum wage, it’s the Iowa contest.

In Iowa, the contrast between the two candidates on the minimum wage is as stark as one could hope for, and the Democrat has emphasized the issue perhaps more directly than any other Dem Senate candidate.

GOPer Joni Ernst has claimed that having a federal minimum wage is “ridiculous,” and has said that $7.25 per hour is a “great starter wage for many high school students,” though economists note that those making the minimum are older than they used to be.

Meanwhile, Dem Bruce Braley has run an ad focused entirely on Ernst’s positions on the issue, particularly her suggestion that she does not support a federal minimum wage. Ernst has tried to backtrack by claiming she never said she’d abolish it, but Politifact dubbed Braley’s ad “mostly true.” The ad also hits Ernst’s suggestion that $7.25 is “appropriate” for Iowa: “Ernst believes Iowans can survive on $15,000 a year.”

A new report issued by the Dem-allied Center for American Progress Action Fund could give Braley more fodder to press the issue. It crunches the numbers from previously-issued reports on the minimum wage, and reaches the following conclusions about the impact a wage hike would have on Iowa — which contrast starkly with Ernst’s pronouncements about it:

* Failing to raise the minimum wage keeps money out of workers’ pockets. Raising the minimum wage to $10.10 per hour would increase wages for 306,000 Iowans by a total of $430,462,000.

* Failing to raise the minimum wage hurts women in particular. 57.8 percent of Iowans who would benefit from a minimum wage hike are women. By opposing raising the minimum wage, Ernst is disproportionately hurting women.

* Failing to raise the minimum wage hurts the economy. Increasing the minimum wage to $10.10 would boost the Iowa economy by $272,483,000.

* Failing to raise the minimum makes it harder for Iowa workers to make ends meet. According to the Massachusetts Institute of Technology, or MIT, a family of three in Des Moines needs $52,362 per  year to meet a minimum standard of living.

The sourcing for these claims is here. That last bullet is far higher than the $7.25 per hour Ernst thinks is appropriate. Indeed, CAP has also commissioned a poll finding 80 percent of Iowans don’t think they could support a household on that wage. A Des Moines Register poll earlier this year found that 65 percent support raising it.

What’s more, the two candidates are vying for the seat of retiring Senator Tom Harkin, who has been a leading champion of the minimum wage hike in the Senate.

National political reporters love the story about Bruce Braley’s dispute with a neighbor over chickens, and the idea that Braley’s “gaffes” have tagged him as “out of touch” has calcified into unshakable fact. It’s true that the race remains tied, and that this is a surprise, given that Braley was supposed to have an easier time against a foe like Ernst.

But Dems remain convinced that her actual views and positions have not yet been sufficiently aired out before the voters. And one close observer of the race, Craig Robinson of the Iowa Republican, believes the polling actually shows that Ernst’s strategy of running a “personality based campaign” has “already run out of gas,” and that “the negative attacks being run against Braley are not as effective as the ads being run against Ernst” — such as the one hitting her on the minimum wage.

In other words, if Braley can make the campaign about issues such as this one, rather than about chickens, that might be the way to prevail over Ernst’s “personality based campaign.” Dems will likely seize on the gap between the facts on the ground in Iowa on the minimum wage — and Ernst’s attention-grabbing quotes about it — to push the campaign in that direction.

Greg Sargent writes The Plum Line blog, a reported opinion blog with a liberal slant -- what you might call “opinionated reporting” from the left.