Some Republicans are none too satisfied with former President Donald Trump’s endorsement of TV celebrity and surgeon Dr. Mehmet Oz over David McCormick, a former hedge fund executive, and spouse of ex-Trump deputy national security adviser Dina Powell, for an open Senate seat in Pennsylvania.

Since Trump publicized over the weekend that he is supporting Mr. Oz, allies, supporters and conservative media figures have raised concerns that the endorsement could hamper Republicans’ chances of winning the crucial battleground state in the party’s bid to retake control of the Senate. They argue that the former daytime TV host lacks conservative policy positions.

The seat, which is being vacated by retiring Republican Senator Patrick Toomey, is one of the few races considered a toss-up by the nonpartisan Cook Political Report. And an average of recent polls compiled by RealClear Politics has Mr. McCormick leading Mr. Oz by less than three points.