Sessions, McConnell and other Republican lawmakers stated that they will need adequate time to fully vet Sotomayor, signaling a potential holdup for Obama, who has said that he wants the new justice confirmed before lawmakers recess in August.
One particular statement that could come back to haunt Sotomayor is one she made while speaking on a panel at the Duke University School of Law in 2005.
In the video from that event, which has popped up on YouTube, she says "All of the legal defense funds out there, they're looking for people with court of appeals experience, because it is, court of appeals is where policy is made," a statement sure to provoke critics of judges who allegedly legislate from the bench. "And I know, and I know this is on tape, and I should never say that, because we don't make law, I know," she continued as the audience laughed. "OK. I know. I know. I'm not promoting it, and I'm not advocating it, I'm, you know."
Though senators confirmed her twice to serve on the federal bench, McConnell and Sessions have both voted against her for past appointments.
But Democrats have the majority of votes in the Senate, and voting against a historic nominee could prove politically difficult for Republicans.
Hispanic groups praised Obama's choice, noting its historical significance and meaning within that community.
Dr. Gabriela Lemus, executive director of the Labor Council for Latin American Advancement and chair of the National Hispanic Leadership Agenda, said Sotomayor's nomination is "history-making" and "smashes another barrier that has stood in the way of Hispanic Americans' full participation in the life of our country."
But Estuardo V. Rodriguez, director of advocacy group Hispanics for a Fair Judiciary, also told ABC News that while the group's members are "emotional about the fact that she's Hispanic," the group wants to emphasize that she is "the most qualified nominee that we've seen, across the board, in 50 years."
Sotomayor's mother, stepfather, brother and his family attended today's announcement, which took an emotional turn when the nominee addressed them.
"I stand on the shoulders of countless people, yet there is one extraordinary person who is my life aspiration. That person is my mother, Celina Sotomayor," she said.
Noting her mother's dedication and strong work ethic, Sotomayor added, "I have often said that I am all I am because of her, and I am only half the woman she is."
ABC News' Viviana Hurtado contributed to this report.