WASHINGTON — Senator Dean Heller, Republican of Nevada, quickly found the limits of party loyalty on Tuesday when a businessman with a famous name in the state announced he was challenging him in a primary.

Mr. Heller, after weeks of publicly agonizing over Republicans’ drive to repeal the Affordable Care Act, stuck with party leadership and voted for a pared-down version of the legislation.

But Mr. Heller’s support was not enough to get the bill passed, as three other Republicans torpedoed the measure.

On Tuesday, Danny Tarkanian, a Nevada businessman and serial candidate for elected office, announced that he would take on Mr. Heller, who was already the most vulnerable Senate Republican incumbent on the ballot next year.