The Florida judge has been on the federal bench for just about a year. She became controversial for not recusing herself from a felon voting rights case.
Brandon Higgs, the white man sentenced, reportedly told the Black man he shot to "go back to Africa." The prosecutor said police found that Higgs has links to white supremacist groups.
Many of Ginsburg's Supreme Court colleagues, including current and former justices, praised her tenure. Chief Justice John Roberts called Ginsburg "a tireless and resolute champion of justice."
The process is shrouded in secrecy, but the president's flair for the dramatic has introduced a sense of showmanship to the highly choreographed roll out.
Judge Alison Nathan wrote she fears government lapses in an Iranian sanctions case may have revealed broader problems with how prosecutors disclose evidence to defendants.
In his statement, Obama said Republicans should "apply rules with consistency, and not based on what's convenient or advantageous in the moment."
Ginsburg, the second woman to serve on the Supreme Court, died from complications from cancer. Her death will set in motion what promises to be a tumultuous political battle over who will succeed her.
Jake Gardner faces four charges, including manslaughter. While local officials initially ruled he had acted in self-defense, a special prosecutor said on Tuesday that new evidence suggested otherwise.