Republicans Want Next President to Fill Antonin Scalia's Supreme Court Seat

— -- Top Senate Republicans said the Senate should not confirm President Obama's nominee to replace the late Supreme Court Justice Antonin Scalia, setting off a charged political battle in Washington amidst the 2016 presidential race.

"The American people should have a voice in the selection of their next Supreme Court Justice. Therefore, this vacancy should not be filled until we have a new President," Senate Majority Mitch McConnell, R-Kentucky, said in a statement today.

Senate Judiciary Chairman Chuck Grassley, R-Iowa, seconded McConnell's thinly-veiled threat to block Obama's choice to replace the conservative justice, who died of natural causes today in West Texas.

"Given the huge divide in the country, and the fact that this President, above all others, has made no bones about his goal to use the courts to circumvent Congress and push through his own agenda, it only makes sense that we defer to the American people who will elect a new president to select the next Supreme Court Justice," Grassley said in a statement.

An aide to Grassley did not say whether the Iowa senator would schedule committee hearings for Obama's eventual nominee.

Democrats bristled at the suggestion that Republicans would keep President Obama from filling the vacancy on the nation's highest court.

"The Supreme Court of the United States is too important to our democracy for it to be understaffed for partisan reasons. It is only February. The President and the Senate should get to work without delay to nominate, consider and confirm the next justice to serve on the Supreme Court," said Senate Judiciary Committee Ranking Member Patrick Leahy, D-Vermont.

Obama said today he intends to put forward a replacement for Scalia.

"These are responsibilities that I take seriously as should anyone," Obama said of his constitutional power to nominate in the case of a vacancy. "They are bigger than any one party."

Sen. Lindsey Graham, R-South Carolina, said in South Carolina that Obama must "find consensus" in a nominee in order to have Scalia's seat filled before he leaves office, and criticized Democrats for changing Senate rules to prevent filibusters of executive office and federal judicial nominees.

"They’re not going to get ... an appointment to the Supreme Court unless they find consensus. They better find it," Graham said.

ABC News' Brad Mielke contributed to this report.