Democratic presidential candidate Hillary Clinton delivers a speech at the 42nd Pennsylvania AFL-CIO Constitutional Convention on April 6 in Philadelphia. (Ricky Carioti/The Washington Post)

PHILADELPHIA — Hillary Clinton launched a fierce new two-pronged attack on rival Bernie Sanders on Wednesday, questioning the persistent challenger's bona fides as a Democrat and his qualifications to run the country.

In comments to a union gathering here and in interviews, the Democratic front-runner did not hide her frustration and annoyance with Sanders and his underdog assault as the once-tame Democratic primary turns increasingly testy.

"We both want to make our economy work for everyone, not just those at the top," Clinton told a union audience here. "But Senator Sanders and I have some real differences about how we would go about achieving our goals as president.

"And like a lot of people, I am concerned that some of his ideas just won't work, because the numbers don’t add up. Others won’t even pass Congress, or they rely on Republican governors suddenly having a conversion experience and becoming progressives," she asserted. "In a number of important areas, he doesn’t have a plan at all."

Clinton has been unable to put the primary phase behind her despite holding a firm lead nationally. Sanders's easy double-digit victory Tuesday night in Wisconsin was only the latest example of his staying power, while a fierce back and forth between campaign aides showed an increasing willingness to attack qualifications and character on both sides.

At a news conference in Philadelphia April 7, Sen. Bernie Sanders (I-Vt.) defended his decision to say Democratic front-runner Hillary Clinton isn't qualified to be president. He said, "If I'm going to be attacked for being 'unqualified,' I will respond in kind.'" (Reuters)

Also Wednesday, Clinton implied that Sanders, a self-described democratic socialist, is not a full Democrat and might not feel the same fealty to the party and its other candidates. The Vermont senator has always caucused with Democrats in Congress but is an independent.

"I think he himself doesn't consider himself to be a Democrat," Clinton said in an interview with MSNBC. "You know, look, he's raised a lot of important issues that the Democratic Party agrees with, income inequality first and foremost. But it's up to the Democratic primary voters to make that assessment."

Speaking from her home in Westchester County, N.Y., Clinton made reference to the April 19 New York primary, which Sanders has recently said he can win. Clinton is trying to effectively end his candidacy with a strong victory in the state she represented for eight years in the Senate. A loss in New York would lend legitimacy to Sanders's claim that he can still catch up to Clinton and become the nominee, perhaps in part by persuading Clinton delegates that she no longer deserves their support.

The argument over who is or is not a Democrat is aimed primarily at elected Democrats, party leaders and activists, many of whom are backing Clinton. As Sanders's campaign has started talking about "flipping" Clinton delegates, she and her surrogates have begun to question Sanders's commitment to the Democratic Party and to other elected leaders.

Clinton supporters note that Sanders has not raised money for the party. Her campaign has recently emphasized how both she and her husband, former president Bill Clinton, have worked to support Democratic candidates for decades. The point has become less subtle as Sanders's recent string of caucus and primary victories — he's won six out of the last seven state contests — has eroded Clinton's still-large lead among pledged convention delegates.

"I've been in the trenches for a long time and I believe in electing Democrats up and down the ticket. I want to see the United States Senate move back into Democratic hands with my friend Chuck Schumer as the majority leader," Clinton said in the MSNBC interview.

She had a similar assessment in another interview published Wednesday. Asked whether Sanders is a "real Democrat," Clinton first hedged, but then made clear that she has doubts.

“Well, I can’t answer that,” she said in the Politico interview conducted last week. “He’s a relatively new Democrat, and, in fact, I’m not even sure he is one. He’s running as one. So I don’t know quite how to characterize him.”

She told the Pennsylvania AFL-CIO convention that any candidate asking for the job of president must be able to show how they would accomplish goals that sound good during the campaign. She suggested that Sanders is more talk than action, pointing repeatedly to her policy-heavy campaign proposals as well as her legislative record, and experience negotiating with foreign governments.

"Sometimes I'm accused of spending too much time on the details of how things actually work, how we get them done," Clinton said. "But if we don’t do that, it would be like negotiating a contract and you walk in and you say to the employer, 'we want a really good deal, so do it.' "

As the audience chuckled, Clinton added: "Not the way I’ve ever seen it work. You've got to know what you want, and you've got to have a plan for getting there."

Earlier, she took a slightly arch tone when discussing Sanders's meandering and sometimes incomplete responses during a New York Daily News editorial board interview this week.

"I think he hadn't done his homework and he'd been talking for more than a year about doing things that he obviously hadn't really studied or understood," Clinton told MSNBC, "and that does raise a lot of questions."

Clinton's comments were far milder than those of her campaign aides, who called the Daily News interview devastating evidence that Sanders has no firm plan for his applause-getting promise to break up the biggest banks.