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

Battle lines are already being drawn over filling the Supreme Court vacancy.

"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.

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."

"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.