Joe Manchin has fallen slightly in a new poll. (AP)

A Republican poll finds that support for Sen. Joe Manchin (D-W.Va.) has fallen since his high-profile push for new gun legislation, but the survey gives little evidence that the decline is related to that proposal.

Mark Blankenship's MBE Voter Opinion Poll has Manchin's approval rating dropping 7 points from March, to a still-high 63 percent. 

However, the poll also finds that 67 percent of voters support Manchin's recent attempt to expand background checks for gun purchases, legislation he co-authored with Republican Sen. Pat Toomey (R-Pa.). Forty-three percent of Republicans and 34 percent of independents oppose the plan, compared with19 percent of Democrats.

In the wake of the legislation's defeat, Manchin has continued to talk to lawmakers and has expressed optimism about another vote. But gun control is not likely to come up again any time soon.

The poll also looked at the race to replace retiring Sen. Jay Rockefeller (D). Rep. Shelley Moore Capito (R) has a 20-point lead over Democratic state Supreme Court Justice Robin Davis in a potential matchup. But Democratic primary voters prefer W.Va. Secretary of State Natalie Tennant to Davis or any other potential candidate, with 40 percent of voters choosing her.

Scott Clement contributed to this report.