With a day to go before the primary election, a Zogby International poll for Reuters/C-SPAN/Houston Chronicle that was taken between Feb. 29 and March 2 shows Obama with 47 percent compared with Clinton's 45 percent. The previous poll from a few days earlier showed Clinton with a narrow 47 percent to 46 percent lead. The same poll showed the race in Texas, which also has its primary Tuesday along with Ohio, Rhode Island and Vermont, narrowing. Obama had a four percentage-point lead several days ago, but that has shrunk slight to a three percentage-point lead at 47 percent to 44 percent.

"The Democratic race has been neck-and-neck in both states, but it has been interesting to watch the volatility under way among Democrats in eastern Texas, which is the swing area of that state," said pollster John Zogby.

In Ohio, Obama has improved his support among men, which Zogby said could be the reason he has moved ahead of Clinton.

Both the Ohio and Texas results in the Zogby poll are within the margin of error of 3.6 percent among the 761 Ohio voters polled, and 3.7 percent among the 748 respondents in Texas.

Other polls show Clinton still maintaining an edge among the two candidates in Ohio, but with Obama gaining ground. Read More