Arkansas Democrats still have to pick their candidate in a June 8 runoff, but for now Republican John Boozman holds sizable leads over both his potential rivals in the state’s U.S. Senate race.

A new Rasmussen Reports telephone survey of Likely Voters in Arkansas, taken Wednesday night, shows Boozman, the winner of Tuesday’s state GOP Primary, with 66% support in a match-up with Senator Blanche Lincoln. The Democratic incumbent picks up just 28% of the vote. Two percent (2%) prefer some other candidate in the race, and four percent (4%) are undecided.

If Lieutenant Governor Bill Halter is his opponent, Boozman, currently the state’s only GOP congressman, earns 60% of the vote to the Democrat’s 33%. Four percent (4%) like someone else in the race, and three percent (3%) remain undecided.

In previous surveys, all the Republican Primary hopefuls outpolled both Lincoln and Halter, generally by double-digit margins.

In short, the race at this juncture is an uphill struggle for the Democratic candidate in a state where the national health care bill continues to rankle voters who register much higher opposition than voters nationwide.

While 56% of voters nationally favor repeal of the health care bill, 72% of Arkansas voters feel that way, including 60% who Strongly Favor repeal. Only 24% oppose repeal, including 18% who Strongly Oppose it.

Boozman earns more than 80% support from the much larger group that Strongly Favors repeal against either Democrat. Lincoln draws 60% of the vote of those who Strongly Oppose repeal, while Halter gets 74% of those votes.

(Want a free daily e-mail update? If it’s in the news, it’s in our polls). Rasmussen Reports updates are also available on Twitter or Facebook.

The survey of 500 Likely Voters in Arkansas was conducted on May 19, 2010 by Rasmussen Reports. The margin of sampling error is +/- 4.5 percentage points with a 95% level of confidence. Field work for all Rasmussen Reports surveys is conducted by Pulse Opinion Research, LLC. See methodology.

Lincoln edged Halter 44% to 43% in Tuesday’s Democratic Primary, but because neither candidate crossed the 50% mark a runoff is set for June 8. Boozman avoided a similar runoff by capturing 53% of the vote out of a field of eight Republican candidates.

Voters not affiliated with either major party favor Boozman by a five-to-one margin regardless of his opponent.

Boozman is viewed Very Favorably by 22% of Arkansas voters and Very Unfavorably by just seven percent (7%).

For Halter, Very Favorables are 11% and Very Unfavorables 29%.

Eleven percent (11%) have a Very Favorable opinion of Lincoln, while 44% regard her Very Unfavorably.

At this point in the campaign, Rasmussen Reports considers the number of people with strong opinions more significant than the total favorable/unfavorable numbers at this point in a campaign.

Only 19% of Arkansas voters are even somewhat confident that Congress knows what it is doing with regards to the nation’s current economic problems. Seventy-seven percent (77%) don’t share that confidence, with 49% who are Not At All Confident.

Seventy-six percent (76%) are also not very or not at all confident that their representatives in Congress are representing voters’ best interests.

Forty-four percent (44%) of voters in the state oppose the confirmation of President Obama’s latest Supreme Court nominee, Elena Kagan. Twenty-three percent (23%) favor her confirmation by the Senate, while 32% are undecided.

Obama lost Arkansas to John McCain in the 2008 election by a 59% to 39% margin, and just 32% of the state’s voters now approve of the job he is doing as president. Sixty-seven percent (67%) disapprove. This is a much higher level of disapproval than Obama earns nationally in the Rasmussen Reports daily Presidential Tracking Poll.

But 72% approve of the performance of Democratic Governor Mike Beebe. Only 28% disapprove of how he’s doing his job.