President Obama should easily win the Democratic primary in Arkansas on Tuesday, but a long-shot candidate could get enough votes to create another embarrassing night in the president's re-election campaign.

A recent independent poll shows Tennessee attorney John Wolfe trailing the president by just seven points â€" 45 percent to 38 percent â€" among likely Democratic voters in the state's largest congressional district, the 4th District. Wolfe is on the ballot statewide.

The primaries Tuesday in Arkansas and Kentucky follow West Virginia's May 8 primary, in which federal inmate Keith Judd took 41 percent of the vote in the Democratic presidential primary.

Political analysts have given a range of explanations â€" from voter dissatisfaction to West Virginia's strong conservative Democratic base. Yet most agree the close finish there and possibly another in Arkansas will have no major impact on Obama winning the national party nomination.

The president has struggled in conservative states, particularly in parts of the Deep South. He took just 39 percent of the vote in Arkansas in the 2008 general election, compared to 59 percent for GOP nominee John McCain.

However, Arkansas has a Democratic governor and helped give native son Bill Clinton two White House terms.

Obama is the only Democratic presidential candidate on the ballot in Kentucky.

The 4th District poll in Arkansas was taken May 10 â€" one day after Obama made public his personal support for same-sex marriage.

The delegates that Wolfe might win will not be recognized at the national convention because he failed to comply with state party rules and didn't submit requisite paperwork.

“Barack Obama's leadership has been shaped too much by the office and too little by the ideals that got him there,” Wolfe, who has little money or infrastructure, says on his official web site. “America needs an alternative. …  The interests of the Pentagon, Wall Street and corporations have dominated Obama's administration. And loyal Americans, taxpayers and small businesses are paying a heavy price as a result.”

Wolf won 12 percent of the vote in the Louisiana Democratic presidential primary in March, and he told the Washington Post he will have to double that number to make an impact in Arkansas.

The Associated Press contributed to this report.