Updated at 4:50 p.m.

President Obama will meet with Senate leaders from both parties next week to discuss the Supreme Court vacancy he must fill, White House Press Secretary Robert Gibbs said today.

Senate Majority Leader Harry Reid, D-Nev.; Minority Leader Mitch McConnell, R-Ky.; Judiciary Chairman Patrick Leahy, D-Vt.; and Judiciary ranking member Jeff Sessions, R-Ala., have been invited to the April 21 meeting at the White House, Gibbs said in a statement.

The meeting will be the first of its kind since Justice John Paul Stevens announced he would retire at the end of the court's term, which is likely to be in June. Obama has offered no timetable for announcing his choice, but White House officials and lawmakers expect him to move quickly, with a goal of having the new justice on the bench when the court's new term begins in October.

Hours before the meeting was announced, Senate Minority Whip Jon Kyl, R-Ariz., suggested Obama's nominee could run into strong Republican opposition if the president used a recent campaign-finance ruling or any other politically charged topic as a litmus test for his nominee.

Kyl's comments on the Senate floor today followed reports that Obama might be looking for a justice willing to overturn the Supreme Court's ruling in Citizens United v. Federal Election Commission that corporations are permitted to directly fund political campaigns. Stevens dissented in the 5-4 decision earlier this year, so a like-minded replacement wouldn't tip the balance.

Still, Kyl said, "You don't go on the bench [saying] 'I'm always going to be against the big guy.'" He did not directly say the GOP would filibuster a nominee, but the comments were in the context of when a filibuster would be justified.

One senator not on the list is former Judiciary Chairman Orrin Hatch, R-Utah. Nor, Hatch said, has the White House consulted him. He called that a mistake.

"Past presidents have called me to advise on nominees, and I'm not complaining, but Obama would benefit if he did," Hatch said. "There's a lot of irritation with the desire to do things the partisan way. I can tell you this, Clinton called me on a lot of things and I always helped. I like this president, personally, and would like to help him as well."