If she becomes president, Hillary Clinton will confront the challenge that Republicans will almost certainly still control Congress. In practice, this means her scope for dramatic new policy achievements is likely to be limited. And it's why the remarks she made Monday morning on prosecuting financial crime are some of the most important words she's spoken thus far in the campaign.

Appointing prosecutors and regulators with a mandate to be tougher than those the Obama administration has put in office is something that she can actually do.

Hillary on misconduct in the financial industry: "There can be no justification or tolerance for this kind of criminal behavior." — Hillary Clinton (@HillaryClinton) July 13, 2015

"Too often it has seemed that the human beings responsible get off with limited consequences...This is wrong—& on my watch, it will change." — Hillary Clinton (@HillaryClinton) July 13, 2015

This speaks to one of liberals' biggest complaints with Eric Holder and the Obama Justice Department — an endless parade of fines with no serious consequences for individual wrongdoing. Elizabeth Warren, among others, has been banging this drum for years without securing any real change in the administration's approach:

"I would have thought that given the things the Department of Justice has been saying about how aggressive they want to get about corporate crime — I would expect to see more corporations prosecuted," Brandon L. Garrett, professor at University of Virginia Law School and author of Too Big To Jail, told Vox last November. "Instead, those numbers have been declining. And I would expect to see more individuals prosecuted in these cases, and very few individuals are prosecuted."

There are significant structural barriers to successful high-level white-collar criminal prosecutions, but whether to at least try is more or less up to the discretion of any given administration.

If a hypothetical future Clinton administration wants to go after more individuals when regulators catch banks breaking the rules, congressional Republicans can't really stop them. At the same time, in the universe of possible ways to get to Obama's left this seems like a pretty safe bet. Wall Street banks are happy to complain about excessive red tape, but no CEO is going to stand up and publicly say that he should be immune from prosecution if his bank is caught laundering money.

Meanwhile, to bank foes the question will be whether Clinton means it. Similar promises to get tough have been made before, only to leave reformers feeling burned by a lack of follow-up, with Obama's second SEC Chair Mary Jo White only the most recent example. Clinton doesn't bear any responsibility for the Obama administration's tendency to go back and forth on the desired severity of enforcement actions, but to activists focused on the issue there is a trust gap. But skeptics should take some succor from the fact that Clinton's practical scope for accomplishment is likely to be sharply constrained. The stakes in 2016 are high, but realistically Clinton is going to want to be remembered as something more than a conservator of the Obama agenda. Demanding tough prosecutions of financial malefactors is a way of leaving a mark that Clinton can actually deliver on.