no desu (or no da or n da) is "a sentence ending which indicates that the speaker is explaining or asking for an explanation about some information shared with the hearer, or is talking about something emotively, as if it were of common interest to the speaker and the hearer" (quoted from _A Dictionary of Basic Japanese Grammar_ by Seiichi Makino and Michio Tsutsui and published by The Japan Times). The ga after desu here is, I think (I say "I think" because you have not given the whole context of the sentence), "a disjunctive coordinate conjunction that combines two sentences", something like "but" in English, e.g., He wants to do it, but I don't. In Japanese the second sentence "is often omitted when it is understandable from the context and/or the situation, or when the speaker doesn't want to continue for some reason (e.g., the sentence is too direct, impolite, embarrassing, etc.)". I hope this answer helps. :)

First of all, "no desu ga" is written "のですが" in japanese, so in alphabet, it should be "nodesuga". No spaces. This expression could be used for a sentence of contrast. For example, "I want to go, but I sleep today." ⇒行きたいのですが、きょうはねます。 　Ikitai "nodesuga"、kyouha namasu。 In this case, "nodesuga" was used as "but". There is also another type of sentence which doesn't have the last half part of sentence. ⇒行きたいのですが・・・ 　Ikitai"nodesuga".....(end) This is a sentence that the speaker is "indicating" that the speaker has a negative condition from the first part of sentence. So that a listener would be able to "guess" that she/he can not go.