WASHINGTON — By the standards of the modern Congress, Representatives Fred Upton, Republican of Michigan, and Diana DeGette, Democrat of Colorado, have no business writing health care legislation together.

Mr. Upton, the buttoned-up chairman of the powerful Energy and Commerce Committee, is one of the House Republicans’ go-to representatives on dismantling the Affordable Care Act. Ms. DeGette, a member of the Democratic leadership who leans decidedly left of center, counts herself among the central champions of the health care law.

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But the two lawmakers, friends since they met in a prayer group nearly two decades ago, have spent the last 18 months — sometimes with a spouse or dog in tow — sitting together through hundreds of hours of meetings with doctors, health advocates and policy experts; traveling to each other’s districts and to policy conferences around the country; and enlisting colleagues coast to coast to hold town hall-style meetings, all with the goal of developing a sweeping measure to help cure diseases.

“Every family is impacted by disease; they just are,” Mr. Upton said. “My wife has lupus, my dad has diabetes, my mom’s a cancer survivor. And I’m no different than anyone else.”