Faced with mounting Democratic retirements on Capitol Hill, the White House is pressuring Senator David H. Pryor (D-Ark.) to run for a fourth term next year. The push comes from fellow Arkansans President Clinton and his senior adviser, Thomas F. McLarty III. Pryor, who suffered a heart attack four years ago, looks like a shoo-in for reelection. But he is wavering on whether to make another run because of health concerns. Democrats fear that his seat is at risk if he leaves. With four Democratic senators already calling it quits, the GOP could win a filibuster-proof majority of 60 in 1996.