No, not even via your simplistic formula is it always clear who 'owns' a bill, PARTICULARLY with Reagan and Bush's genesis and incubation of NAFTA respectively, together with more GOP than Dem votes in both chambers for NAFTA.
IF Reagan had proposed the ACA, with the public option that Obama wanted, and Dubya had picked it up and ran with it over his 8 years, and GOP votes matched their NAFTA votes, and Obama signed it in '09, giving up the public option, really think the GOP would be trying to overturn it as late as 2017?
Simple really, even more so, Presidents and their party own their bills, right?
Obama = ACA
Clinton = NAFTA
It was a weird vote, more repubs than dems.....Wont see a mixed up vote like that again