[We have one of the last centrist politicians on the red side.]
As a centrist I wouldn't call Murkowski a centrist.  Firstly, centrism isn't "middle of the road," "fence-sitting," etc. but a ideology that we as a nation and as a result of our governing system got to where we are with good reason.  This generally means resisting any big shifts one way or the other.
Secondly, Murkowski is consistently conservative in about 90% of her stances.  There are two areas she consistently breaks from her party though.  Namely reproductive rights and hate crimes.  But for gun rights, gay marriage, pro-development, etc. etc. etc. even affirmative women's rights Murkowski votes alongside most Republicans.
I don't think Murkowski's issue on the Republican healthcare bill is shifting the healthcare issue a good distance to the right so much as the disregard for proper process and inclusion of viewpoints.