I don't think that's what is bothering NATO, it's Trump's failure to verbally affirm Article 5 of the NATO Treaty.
On the issue of defense spending, different members of NATO have different economic hardships. Do we really expect Greece to crank up defense spending while in a debt crisis and under heavy austerity already? These NATO guidelines have to be somewhat contextual based on reality of economics.
Gates said the same thing, in fact he said that the US basically cannot not afford another war unless it's attacked on its own soil and if NATO will not pick up the slack the US will be forced to reconsider its part in the partnership.
This was said in Brussels in front of all of NATO.
The EU have been skimping on its NATO commmitments since the end of the Cold War this isn't a recent development.
Greece is actually meeting it's goals (likely because of its sick waving contest with Turkey) while Germany, France, Italy and even the U.K. do not.
As for Article 5 there has been already blood in the water since Iraq.
France basically said that if the US uses Article 5 for Iraq it will ignore it, Germany and Italy were also signaling the same sentiments.
Well, in the case of Iraq though, it seems a slam dunk, since Iraq had not attacked any NATO member.
If the US wants other NATO members to step up, then they should reduce payments. Either NATO members will make the determination that the new budget constraints represents an unacceptable level of reduction in capability below which they think is required, or they'll think NATO doesn't need as large a budget.
Realistically, NATO's deterrence effect against Russia comes down to nuclear-MAD. The conventional forces don't matter as much, if NATO is attacked by Russia conventionally, and NATO goes to war, you have a direct hot war between two nuclear equipped entities which is a bit too much risk, so there's little chance of a Russian invasion of a NATO member regardless of NATO conventional defense capabilities.
I think it's likely any conflicts with non-NATO states on the Eurasian continents will likely be proxy conflicts, with NATO and Russia backing different factions, like with the Korean War, Vietnam, and Afghanistan.
Trump's remarks are not new these are the same remarks that have been thrown around since Busb senior was in office.
Heck Under Obama Sec Def Gates used much harsher words than Trump.