Was every Jew in the Old Testament meant to be a priest?
Yes. According to Exodus 19:6, Israel was called to be a kingdom of priests and a holy, set-apart nation. The context explains that in God's Old Testament program every Jew was to have become a priest of God, not merely the Levites for tabernacle worship, but as go-betweens reaching out to Gentiles.
Les explains that Exodus 19:6 is a benchmark verse: God told Israel that if they were obedient to His covenants, they would be a treasure above all other nations, a kingdom of priests, and a holy nation. He says this was more or less prophetic, pointing to a future day when every Jew was to have been a priest of God. While the Levites had their role so far as tabernacle worship was concerned, Les clarifies that the larger issue was Israel reaching out to Gentiles. Every Jew in God's Old Testament economy was to have become a priest. A priest, he notes, is a go-between.
And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.