Even before taking the stage to thank her supporters Tuesday, Hillary Clinton took to Twitter celebrating a milestone as she comes closer than any woman has ever come to being the presidential nominee of a major political party.

"We made history tonight," Clinton said in one Tweet, promoting a free magnet bearing her image which reads, "June 7, 2016: History made."

Another Tweet touts, "Tonight, we can say with pride that, in America, there is no barrier too great and no ceiling too high to break."

Her positive tweets came around the same time that presumptive Republican presidential nominee Donald Trump used his victory speech on Tuesday to attack Clinton, saying she "turned the State Department into her own private hedge fund."

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 Speaking after his wins in New Jersey, South Dakota and New Mexico from one of his golf courses in suburban New York City, Trump also said he would be giving a major speech about the Clintons, "probably Monday."

Trump spoke a short time before Clinton won the Democratic presidential primary in New Jersey on Tuesday, adding to her lead in pledged delegates and contests won over rival Bernie Sanders.

However, Sanders received the majority of delegate support in North Dakota. 

It was the first of six states to cast ballots in presidential primary contests Tuesday, but many were clearly looking ahead to the general election.

Clinton reached the 2,383 delegates needed to become the presumptive Democratic presidential nominee on the eve of Tuesday's voting, according to an AP tally. The AP count shows Clinton had 1,812 pledged delegates and the support of 571 of the 714 superdelegates.

Superdelegates are able to change their vote at the convention.

Earlier, voters in Democratic and Republican primaries told The Associated Press they have long been weighing and comparing candidates of both parties with an eye toward who would make the best general election candidate in November.

Tuesday's elections in New Jersey, California, Montana, New Mexico, North Dakota and South Dakota featured a contest between Clinton and Vermont U.S. Senator Bernie Sanders, who is urging superdelegates to drop their support for Clinton, arguing he is a stronger candidate to take on Trump.

Republican presidential candidate Donald Trump used a victory speech Tuesday to attack likely Democratic candidate Hillary Clinton, saying she used the State Department as 'own private hedge fund." (MartAssociated Press)

What voters are saying

Tuesday's elections in New Jersey, California, Montana, New Mexico, North Dakota and South Dakota feature a contest between Clinton, the former secretary of state, and Sanders, who is urging superdelegates to drop their support for Clinton, arguing he is a stronger candidate to take on Trump.

In San Diego, 82-year-old Harry Backer strolled past cyclists, skateboarders and kayakers on the way to vote for Clinton. The retired teacher, who also worked in construction, said America needs a level-headed, grounded woman with world experience.

"I'm left of Bernie Sanders, but I know that she's the candidate that can possibly get something done," Backer said.

He also wanted to be part of history in making Clinton the first woman to top the ticket of a major U.S. political party.

In Albuquerque, N.M., Lucy Demir voted for Sanders.

"I like him because he's really honest," said Demir, 37. "I think he's really direct, and I appreciate how he really is trying to stay on his side of the street. I actually think some of his ideals are kind of like utopic and he's probably not going to achieve them, but I like his character."

In Closter, N.J., an upscale suburb, Izabela Biel voted for Trump, saying his success as a businessman symbolizes the American dream for her. Biel came to the U.S. from Poland about 25 years ago, and she said that even though he isn't the perfect candidate, she prefers him to the Democratic candidates, who "want to make everybody equal."

"I grew up in communism," said Biel, 46. "I've lived it, and I absolutely know that it's proven that it doesn't work. You can't make everybody equal; that just doesn't exist in the real world."