Well, I can figure why some Spanish native speakers felt a language barrier in a city like Barcelona.
That won't happen in Valencia. In the city, 99% of people speaks Spanish, and Spanish is the everyday language. You'll see advices written in Valenciano everywhere, but the Advices are generally bilingual (Spanish-Valenciano).
Of course, sometimes you'll hear people speaking in Valenciano, but if you talk to them and they realize you don't speak Valenciano they will speak in Spanish to you 99% of the times (or should I say 100%?.. well, "por si acaso"). You won't find in Valencia the language barrier that you may find in Barcelona.
In many of the Pueblos and small Towns surrounding Valencia, people use to speak Valencian as mother tongue, but they'll also speak to you in Spanish if they realize you don't understand.
As you see, there are two areas: the city itself (99% Spanish speaking) and the province (great percentage of native Valencian speakers), but the people attitude is very similar to non-Valencian speakers.
As well, the Valencian, although being a variation of Catalan, has not the ideological charge that Catalan has in Cataluña to many people, and the valencian people's attitude is different. I don't mean better (although you can easily imagine my opinion, but...), just different.
Don't worry about that, you can perfectly live in Valencia without knowing a word in valenciano. Situation is not comparable to Cataluña at all.