Cruz described the Supreme Court vacancy left by Scalia as having a "profound impact" on the Republican primary that will change the contours of the presidential race. He argued voters -- not a "lame-duck president" -- should decide who will replace the longtime conservative judge who died Saturday.
"This is a 5-4 court -- the next election needs to be a referendum on the court," Cruz told ABC News' George Stephanopoulos. "People need to decide."
President Obama said Saturday he planned to nominate a replacement for the vacancy on the Supreme Court. Cruz said he would "absolutely" filibuster before the Senate could vote on the nominee.
"This should be a decision for the people," Cruz said. "Let the election decide. If the Democrats want to replace this nominee, they need to win the election. But I don’t think the American people want a court that will strip our religious liberties. I don’t think the American people want a court that will mandate unlimited abortions on demand, partial birth abortion with taxpayer funding and no parental notification and I don’t think the American people want a court that will write the Second Amendment out of the Constitution."
Cruz used the Second Amendment issue to appeal to South Carolina's veterans and jab at his fiercest rival in the state -- Donald Trump.
"If Donald Trump becomes president, the Second Amendment will be written out of the Constitution because it is abundantly clear that Donald Trump is not a conservative. He will not invest the capital to confirm a conservative, so the result will be the same whether it’s Hillary [Clinton], Bernie [Sanders] or Donald Trump," Cruz said. "The Second Amendment will go away."
Cruz, who clerked for former Chief Justice William Rehnquist and argued many cases in front of the Supreme Court as solicitor general of Texas, attempted to contrast his judgment with Trump's.
"Anyone that writes checks to Chuck Schumer and Harry Reid and Jimmy Carter and Hillary Clinton does not care about conservative justices on the court," Cruz said. "Donald Trump himself, you know, the one person he has suggested that would make a good justice is his sister, who is a court of appeals judge appointed by Bill Clinton. She is a hardcore pro-abortion liberal judge and he said she would make a terrific justice."
Trump has said he would not nominate his sister because it would be a conflict of interest, and said he was joking when he mentioned her as a potential nominee.
Cruz also hit at Trump following Saturday's debate in South Carolina, saying it showed the real estate mogul isn't a conservative.
"He defended Planned Parenthood and federal taxpayer funding for Planned Parenthood on the debate stage," Cruz said. "He said he thinks they do terrific things. I don't think Planned Parenthood does terrific things."
The two sparred during the debate with Trump calling Cruz a liar and Cruz saying Trump relies on insults to stop discussions about his record.
Cruz added one more jab at Trump for not disavowing a past remark he made that he would have impeached President George W. Bush over the war in Iraq.
"That is not consistent with the Constitution and those are the views of the fever swamps of the left. That's where Donald comes from is the fever swamps of the left," Cruz said Sunday on “This Week.” "He's supporting John Kerry and saying let's impeach George W. Bush. That is not a commander-in-chief fit to keep this country safe."