Clinton, fighting to save her presidential bid after 11 straight wins by Obama, desperately needs victories in the big-state battles to keep her candidacy alive and face the Republican candidate in the November election.
Obama, an Illinois senator, has a slim advantage on Clinton in both states, although the leads are within the poll's margin of error of just under 4 percentage points.
Obama leads 47 percent to 44 percent in Texas, as Clinton gained 1 point overnight in the polling conducted by Zogby International. He leads 47 percent to 45 percent in Ohio, a turnaround from Clinton's 1-point advantage on Sunday.
Obama has wiped out big leads in the last two weeks in both states for Clinton, a New York senator and former first lady, but in the final days of the race neither candidate has managed dramatic shifts.