During an interview on ABC's "This Week," Cruz told ABC News Chief Anchor George Stephanopoulos that the nation cannot afford to have a short-handed high court with a possible contested presidential election just 44 days away.
Cruz began the interview by saying he and his wife's prayers are with the Ginsburg family, "who are grieving the loss of someone who led an extraordinary life."
"She was a trailblazing advocate, one of the finest Supreme Court litigators to have ever lived," said Cruz, adding that as a lawyer he argued cases before Ginsburg nine times. "She was a brilliant justice. Her questions were always incisive. She was a careful lawyer."
Turning to the issue of replacing Ginsburg, Cruz, when prodded, said, "I believe the right thing to do is for the Senate to take up this nomination and to confirm the nominee before Election Day."
When Stephanopoulos pressed Cruz on whether the Republicans have the votes to push Trump's nominee through, Cruz hesitated.
"I don't know the answer to that," Cruz said. "I believe we will."
Ginsburg, one of four justices who made up the Supreme Court's liberal wing, died on Friday at the age of 87 due to complications from her battle with pancreatic cancer.
NPR reported that just days before her death, Ginsburg dictated a statement to her granddaughter Clara Spera, saying, "My most fervent wish is that I will not be replaced until a new president is installed."
But just hours after Ginsburg died, Senate Majority Leader Mitch McConnell, R-Ky., said Trump's pick to replace Ginsburg will get a vote on the Senate floor, prompting backlash from Democratic leaders, including Senate Minority Leader Chuck Schumer, who described McConnell's decision as the "height of hypocrisy."
When Obama nominated U.S. Circuit Court Judge Merrick Garland in 2016 to fill the seat of Justice Antonin Scalia, the conservative lion of the Supreme Court who had died, McConnell and the majority of his Republican Senate colleagues refused to grant a confirmation hearing 10 months before the presidential election, saying the next president should make the appointment.
At the time, Cruz was running to be the Republican presidential nominee and released a statement, saying, "I proudly stand with my Republican colleagues in our shared belief -- our advice and consent -- that we should not vote on any nominee until the next president is sworn into office."
Now Cruz and many of his Republican colleagues have a different take.
"In this instance, the American people voted. They elected Donald Trump. A big part of the reason they elected Donald Trump is because of the Scalia vacancy and they wanted principle constitutionalists on the court," Cruz said Sunday. "And so the president was elected to do this and the Senate was elected to confirm this nomination."
Republican Sens. Susan Collins of Maine and Lisa Murkowski of Alaska have gone on the record saying they oppose voting on a nominee before the November election.
Stephanopoulos asked Cruz "whether you're in step with most Republicans right now in voting before the election?"
"Sen. McConnell seems to have not made up his mind on whether that's best for your majority. You're pushing him here, right?" Stephanopoulos asked.
Cruz responded by bringing up President Jimmy Carter's nomination of Stephen Breyer to an appellate judgeship after Carter lost the election in 1980 to Ronald Reagan.
"You know what the Democratic Senate did? By the way, the voters had just thrown the Democratic Senate out and said we're going to have a Republican Senate. The Democratic Senate took it up in December and confirmed it in the lame-duck," Cruz said of Breyer’s nomination.
Breyer was later appointed to the Supreme Court by President Bill Clinton.
"There's a long history here, and everybody knows if the president were Joe Biden or Hillary Clinton, and Chuck Schumer was the majority leader, the odds are 100%" that they would put a nominee to a vote, he said.
Earlier on "This Week," House Speaker Nancy Pelosi said, "We have arrows in our quiver" to use in an attempt to block Trump's pending nomination.
Cruz responded that Pelosi would have supported a nomination if the roles were reversed and a Democrat was now in the White House.
Cruz said the country is facing a "serious risk of a constitutional crisis" if the upcoming presidential election is contested.
"Joe Biden has been explicit. He has said if he doesn't win he's going to challenge this election," Cruz said, adding that Biden has already assembled a legal team to challenge the election if he loses and that Hillary Clinton has advised him not to concede the election.
Stephanopoulos challenged the accuracy of Cruz's statement.
"It's been President Trump who is the one talking about rigged elections," Stephanopoulos said. "Joe Biden has not explicitly said he's going to challenge the election. Of course, they're going to have teams of lawyers, as every campaign always does, to look at irregularities."
Cruz went on to say that the Supreme Court, now comprised of five conservative justices and three liberal justices, needs to operate at full capacity if there is a challenge to the election.
"An equally divided court, 4-4, can't decide anything," said Cruz, assuming there is a deadlocked outcome. "That could make this presidential election drag on weeks and months and well into next year. That is an intolerable situation for the county. We need a full-court on Election Day given the very high likelihood that we're going to see litigation that goes to the court. We need a Supreme Court that can give a definitive answer for the county."
But back in 2016, Cruz, speaking to reporters on the campaign trail, cited "precedent" for a Supreme Court with fewer than nine justices.
"You know, I think there will be plenty of time for debate on that issue," Cruz said at the time. "There is certainly long historical precedent for a Supreme Court with fewer justices. I would note, just recently, that Justice Breyer observed that the vacancy is not impacting the ability of the court to do its job. That's a debate that we are going to have."