During the question and answer portion of her event in a rural town in northern Nevada, the Democratic presidential candidate also tipped her hand on people Obama would consider.
"I think the President's going to look for somebody who has a record that is gonna be hard for the Republicans to be against," said Obama's first-term secretary of state. "Somebody who is a sensible person with a good record and maybe somebody who's already been confirmed by the Senate."
"We've got some judges on the courts of appeals, they were confirmed 99 to nothing," Clinton said. "So there people who have already gone through the process."
She added, "There are some great other people, great jurists and lawyers and advocates. So I'm hoping that we get somebody nominated and everybody will say, 'Hey, the only reason to block this is pure partisanship, and so do your duty. This person is well prepared.' "
Justice Antonin Scalia died in Texas on Saturday, setting up what has become a premier political battle. Republicans quickly moved to say Obama should not nominate a justice and called on him to wait for the 2016 election to be decided. Likewise, Democrats responded by arguing the President has the authority and the right to nominate a justice, even if the opening happens in his last year in office.
Hours after Scalia's death, Clinton used a speech in Denver to blast Republicans for suggesting Obama can't nominate a successor to the court, all but guaranteeing the issue will become a key fight in 2016.
"Barack Obama is president of the United States until January 20, 2017," Clinton said. "That is a fact, my friends, whether the Republicans like it or not. Elections have consequences. The President has a responsibility to nominate a new justice and the Senate has a responsibly to vote. And all of us Democrats, we have a responsibly to make sure a Republican doesn't win in November and rip away all of the progress we have made together."
Clinton on Sunday declined to say who would be on her Supreme Court short list when asked by CNN.
Clinton continued to press Democrats in Nevada to make the Supreme Court a political issue on Monday, telling supporters in Elko that Democrats need to make obstructionism in Congress a galvanizing issue in November.
"We Democrats have a chance to take back the Senate," Clinton said before noting that Democrats running in more moderate states like Illinois, Pennsylvania and New Hampshire should be able to use obstructionism in Congress as a "voting issue."
Clinton has spent the past three days traveling through Nevada in an effort to shore up support ahead of Saturday's caucuses. Clinton's campaign, once confident that Nevada would be a win for them, has grown more worried in recent weeks, particularly after Vermont Sen. Bernie Sanders' landslide New Hampshire primary victory.