No, Oregon is very culturally liberal, which, in my opinion, I can't see the GOP winning over. All the GOP has to do is do better with Hispanics (which they can easily do, but their image is killing them right now) and they'll do lots of improvement (since the state is almost majority Hispanic). New Mexico is closer to the GOP PVI wise as well.
Current registration party enrollments in New Mexico (as of August 1, 2013) are:
Democrats: 47%
Republicans: 32%
Independents: 18%
Other parties: 3% (I guess these are mainly Libertarian voters)
So even if every independent New Mexico voter would vote for the Republican presidential candidate, that candidate would just barely win the state.
All independents voting Demcratic would end in this landslide: D 65% - R 32%
All independents voting Republican instead would squeak out a victory for the other side: R 50% - D 47%
The equivalent party registration in Oregon (as of August 1, 2012) are these:
Democrats: 39.5%
Republicans: 31%
Independents: 22.4%
Independent Party of Oregon (started in 2007): 4.4%
Libertarians: 0.7%
Green: 0.5%
Other parties: 1.5%
An interesting study found that Oregon has the most liberal voters in the US (more so than Vermont or D.C.), at the same time it
also has the most conservative voters in the US (more so than Utah or Tennessee). This of course, makes Oregon the most polarized state in the entire US, at least by this approach.
It's not even a racial thing in Oregon, as it would be in Mississippi and many other states. We're mostly talking extremely liberal whites versus extremely conservative whites.
So yes, it seems that New Mexico has already outgrown Oregon as the more Democratic-friendly state of the two, at least by these numbers, taking party registration into account.