A Wall Street Journal/NBC News poll published Thursday showed that Clinton, was favored by 36 percent of respondents, while Obama came in at 31 percent, and 2004 vice presidential nominee former Sen. John Edwards, D-N.C., had 20 percent support.
In March, Obama was 12 percentage points behind Clinton in the Journal/NBA News poll.
Obama "seems to be gathering momentum as the candidate of change," Neil Newhouse, the Republican pollster who helped with the poll, told the newspaper.
The Democrats seeking the party's 2008 nomination for president are to meet Thursday in a debate in South Carolina.
Among Republicans, former New York City Mayor Rudy Giuliani showed 33 percent support, down from 38 percent last month. U.S. Sen. John McCain, R-Ariz., had 22 percent, down from 24 percent in March.
Former Sen. Fred Thompson, R-Tenn., who is considering joining the Republican race for the nomination, showed 17 percent of the support.
The Wall Street Journal reported that the survey results suggest that Americans are beginning to agree with Senate Majority Leader Harry Reid, D-Nev., on the the Iraq war; 55 percent of respondents said victory in Iraq is not possible.