SIKESTON, Mo. — Senator Claire McCaskill freely admits the squeeze she finds herself in these days, with a re-election battle looming next year in a state that President Trump won by 19 points.

“Some of you think I’m some tool for the left,” she matter-of-factly told the crowd at a town hall-style meeting here this week. “Some of you think that I’m a sellout because I’m not left enough.”

Ms. McCaskill would prefer another label — moderate — or perhaps a longer description: someone who can bring polarized partisans together in the middle and therefore is well worth sending back to Washington, even for voters in a state that has moved decidedly rightward in its politics.

As a vulnerable Democrat in an increasingly red state, Ms. McCaskill is hoping that her meet-in-the-middle politics will lead to a third term, even after Mr. Trump’s success last year. But first, she must determine how exactly to approach his presidency.