Washington (CNN) Donald Trump called on Supreme Court Justice Ruth Bader Ginsburg to resign early Wednesday morning, joining an outpouring of criticism that is giving a divided Republican Party a fresh common target.

"Justice Ginsburg of the U.S. Supreme Court has embarrassed all by making very dumb political statements about me. Her mind is shot - resign!" Trump tweeted.

But other top Republicans who have never shied away from criticizing liberal Supreme Court rulings aren't going as far as to say Ginsburg should quit.

"I'm not prepared to say that," Texas Sen. John Cornyn, Senate majority whip, told CNN. "I think she should reconsider and change her course of conduct because I think she's got into an area that is out of her control.. And that I think will reflect poorly not only on her but on the objectivity that we request and demand out of our federal judiciary."

Sen. Orrin Hatch, the senior member of the Judiciary Committee and longest-serving GOP senator, said: "Those comments were inappropriate. On the other hand, she's reached a point in her life that she ought to say whatever she wants to."

The 82-year-old Hatch added: "The older we get the more crusty we can be."

Senate Judiciary Chairman Chuck Grassley, R-Iowa, would not call on Ginsburg to resign.

"I think that it was the wrong statement, she ought to apologize for it, she ought to withdraw it," Grassley said Wednesday when asked about Trump's demand.

Even Texas Sen. Ted Cruz, Trump's old primary rival and a sharp critic of Ginsburg, stopped short of calling her to resign.

"Her comments were obviously inappropriate," Cruz said in the Capitol. When unelected judges try to impose their own policy views ... it's wrong and it's dangerous."

Ginsburg, in an interview Monday evening with CNN legal analyst and Supreme Court biographer Joan Biskupic, called Trump a "faker" and said he had "no consistency about him."

The liberal justice made similar remarks to The Associated Press and The New York Times in recent days.

Democrats have largely given her a pass so far. Democratic Senate leader Harry Reid declined to answer directly when asked about Ginsburg on Tuesday. Reid emphasized Senate Republicans' refusal to consider President Barack Obama's choice to fill an open seat, Merrick Garland.

"I'm not going to comment on what any of the eight Supreme Court justices say," he told reporters.

When asked about the firestorm, White House Press Secretary Josh Earnest replied, "She didn't earn the nickname the notorious RBG for nothing."

Earnest said he declined to comment further- pointing to past precedent.

"In the past I've been asked about controversial comments from other Supreme Court justices, earlier -- I don't know if it was early this year or at the end of last year when Justice Scalia made some comments in an open Supreme Court hearing that many found to be quite controversial, possibly even racist," Earnest said, apparently referencing comments Scalia made in December regarding black college students . "At that point I declined to weigh into that criticism. I think I'll pursue a similar approach in this instance."

Sen. Patrick Leahy of Vermont, ranking Democrat on the Judiciary panel, said: "I guess (Trump) was upset because she pointed out that he lied about disclosing his tax returns. So I'll let them worry about that.

"I don't recall Republicans getting upset when Justice Alito went to a Republican fundraiser before the re-election of Biden and Obama and attacked Joe Biden there," he added. "Maybe they have different standards. I don't know."

Trump also told The New York Times that the comments were "highly inappropriate."

"I think it's highly inappropriate that a United States Supreme Court judge gets involved in a political campaign, frankly," he told The New York Times. "I think it's a disgrace to the court and I think she should apologize to the court. I couldn't believe it when I saw it."

House Speaker Paul Ryan on Tuesday also sharply criticized Ginsburg.

"I find it very peculiar, and I think it's out of place," Ryan told CNN's Jake Tapper during a CNN town hall. "For someone on the Supreme Court who is going to be calling balls and strikes in the future based upon whatever the next president and Congress does, that strikes me as inherently biased and out of the realm."

Ryan said that someone in an appointed branch of government -- and especially someone who will have to adjudicate cases in the future where the administration is a party -- should not critique presidential candidates.

Florida Sen. Marco Rubio suggested Wednesday that the comments were a sign Ginsburg couldn't be "impartial."

"How can a #SCOTUS justice involved in partisan attacks during campaign be impartial in any cases involving a Trump administration?" Rubio tweeted.

Speaking to reporters on Tuesday, Senate Majority Leader Mitch McConnell called her comments "totally inappropriate."

Ben Carson, a Trump confidant, told CNN's Erin Burnett on "OutFront" that he agreed.

"It is completely inappropriate for Supreme Court justices to inject themselves into a political campaign, no matter what side they're on," Carson said. "Because we're already suspicious about the way the Supreme Court is going."

Trump wasn't done criticizing Ginsburg Wednesday evening as he hit her in a series of tweets.

"Is Supreme Court Justice Ruth Bader Ginsburg going to apologize to me for her misconduct? Big mistake by an incompetent judge!" Trump wrote in one message.

Is Supreme Court Justice Ruth Bader Ginsburg going to apologize to me for her misconduct? Big mistake by an incompetent judge! — Donald J. Trump (@realDonaldTrump) July 13, 2016

"If I win the Presidency, we will swamp Justice Ginsburg with real judges and real legal opinions!" he added.