Toras Chaim - compendium of statements attributed to Rav Chaim on Parsha. This is from Beshalach, p. 67 “Mie’amtem Lishmor mitzvosai vesorosai.” (Shemos 16:28)
Chulin 5a says a mechalel shabbos is like an oveid kochavim; see Rashi there. Tashbatz III:43 writes that the Baal HaItur that that chilul shabbos is only by working the land (avodas karka), and Beis Yosef quotes this in E”H 44. The Netziv asks if this Baal HaItur holds like the Geonim who learn it from (Shemos 31:13) ach es shabsosai tishmoru, if so, why is avods karka different than other melachos? Therefore it seems the source for the Itur is in Mishpatim (23:12) 6 days you will do your work and on the seventh you will rest...and keep everything I told you, and the name of another god you shall not mention.” From this we learn that a mechalel shabbos is like oveid a”z and denies the entire torah, that “do your work” refers to avodas karka because it is talking about shmitta (i.e., agricultural laws) there.
Rav Chaim explained this matter based on Yerushlami Nedarim (end of 3rd chapter) “In Torah, Neviim and Kesuvim we find that Shabbos is equal to all the other mitzvos in the Torah as it says “ad anah mei’antem lishmor mitzvosai vesorosai.” And it is written: “Re’u ki Hashem nasen lachem hashabos...” We see that the pasuk that they did not keep shabbos and they went to gather Mon on Shabbos “mei’antem lishmor mitvosai vesorosai,” implying that not keeping shabbos is like transgressing all of the mitzvos of the Torah, and this language is also written by idolotry in Bamidbar 15:22 “vechi sisgu velo saasu es kol hamitzvos ha’eileh,” which also sounds like you transgress the entire Torah.
However, Shavuos 29a that Tzitzis is equal to all of the mitzvos, is not like Shabbos. Because by tzitzis it doesn’t say it in the negative; it does not say if you don’t keep tzitzis it is like you have transgressed all of the mitzvos of the Torah. However, by Shabbos and Avodah zarah it does make the negative comment.
Source: Netziv, Harchev Davar, Ki Tisa 31:17; Mishulchan Gevohah II p. 104. (ad kan Toras Chaim.)
The Baal HaItur is also cited by Rabi Akiva Eiger, Y”D 2:5
My Rebbi shlit"a discussed this on 11 Adar I 5768: Why does the Itur hold you're only a mumar if you do avodas karka?
I suggested that the source is “ha’aretz” in Ki Sisa. My Rebbi explained that Shabbos commemorates both the creation of the world and yetzias mitzraim. This parsha mentions both- 31:13 is yetzias mitzraim, and pasuk 17 for in 6 days I created the world... And meforshim say shabsosai (plural) includes Yom Tov.... In summary, 2 parts to shabbos: Yom Tov is identical to shabbos in commemoration of yetzias mitzraim. But the Melachos we can figure out ourselves is zecher lemmasei breishis. Once we say there are two elements to shabbos, we can suggest passuk 17, os hee - lemaaseh breishis, and creation is like avodas karka, which are known without Mishkan.