Alexander Hamilton graces the  front of the U.S. $10 note in 2009. (Karen Bleier/AFP/Getty Images)

The Treasury Department's plan to bump Alexander Hamilton and put a woman's portrait on the $10 has run into some pretty strong criticism in recent weeks, especially from those who believe it might be better to target another currency portrait -- Andrew Jackson's $20 -- instead.

On Wednesday, Treasury Secretary Jack Lew responded to that criticism, arguing that Americans have "waited long enough" to see a woman's face on paper money, and that changing the portrait on the $10 is the fastest way to make it happen.

Lew was speaking at the Brookings Institution on Wednesday, mainly about Dodd-Frank, when a moderator asked him about pushback from, among others, Hillary Clinton, on the department's decision.

"I will say that what we meant to do is to trigger a broad public debate," Lew joked when asked about the pushback against the choice of the $10, "and we have triggered a broad public debate."

U.S. Treasury Secretary Jack Lew announced that a woman will be featured on a new $10 bill rolling out in 2020. Here are four likely candidates. (Nicki DeMarco/The Washington Post)

"We are committed," he added, "to making a decision that will put a woman on our currency and will do it as soon as possible." Lew said that the Treasury Department follows a "sequence" governing the redesigns of American paper currency, and that the next bill up for a redesign is the $10.

"I think we have waited long enough," he said, adding that the department intends to continue  "honoring" Alexander Hamilton on the bill.

The Treasury Department announced in June that it would put a woman's portrait on the $10 in 2020, and would spend the summer collecting suggestions from the public on which woman should appear on paper money for the first time in about a century. Although the department has said that it's possible Hamilton, who was the country's first treasury secretary, would still appear on the bill in some form after the redesign, the change is clearly a demotion for Hamilton.

[A woman will appear on redesigned $10 bill in 2020. Who will it be?]

Lew said in June that the $10 was the next bill due for a redesign, and that proceeding with a plan to feature a woman on that bill would be the quickest way to accomplish the goal of putting a deserving woman from history on paper money. But the announcement followed a popular campaign targeting another denomination -- the $20 -- and the more controversial figure whose face graces that bill: Andrew Jackson. 

It seems that the call to replace Jackson instead of Hamilton has stuck around past the Treasury Department's announcement. 

"As many have pointed out, a better solution is available: Replace Andrew Jackson, a man of many unattractive qualities and a poor president, on the twenty dollar bill. Given his views on central banking, Jackson would probably be fine with having his image dropped from a Federal Reserve note."

Others, including multiple editorial boards of major newspapers, have agreed: It should be Jackson, and not Hamilton, who makes way for a woman.

[Why is Andrew Jackson on the $20 bill? The answer may be lost to history.]

An independent campaign that asked the White House to consider kicking Jackson off of the $20 and replacing him with a woman raised the issue  this year. The campaign -- dubbed "Woman on $20s" -- eventually chose Harriet Tubman as the woman they'd most like to see on the $20.

As of now, the Treasury Department has given little indication of which women are being considered for the honor on the $10.

But here are some of our ideas.