Mosaic Or Sinai Covenant
The Sinai covenant was far more extensive than the covenant God made with Abraham. At Sinai a formal priesthood, government and set of national laws were put in place. The potential for more material well being was introduced and some specific punishments for disobedience were included in the covenant. Those punishments dealt with time.
Many Christians mistake the entire series of Old Testament covenants as the "Old Covenant." This is not so. The Sinai covenant alone is referred to in the New Testament as the Old Covenant.  The Book of Hebrews goes into extensive detail about how the New Covenant supersedes the ceremonial law introduced at Sinai. Similarly, the New Testament explains that the New Covenant is simply what Abraham was looking forward to and that Christians have covenantal relationship to God's promises through Abraham's covenant. 
The motivation for the events surrounding the Exodus from Egypt was God's remembering of the covenant he had entered with Abraham. Through a long series of events that lead to a visitation of God at Mount Sinai the ancient nation of Israel was delivered from bondage and taken out of Egypt.
At Mount Sinai the nation entered into another Covenant. The summary of that covenant is recorded today in Leviticus 26, sometimes called the "blessing and cursing" chapter.
What God would do on Israel's failure
Though we consider the Sinai covenant to be a conditional covenant, breaking of the covenant in no way made the covenant non-binding. There was no way ancient Israel could escape the covenant, the covenant itself did not provide any escape clauses. Instead, by not keeping their part of the bargain ancient Israel shifted into clauses in the covenant that involved some very specific punishments, the most important for our study here involved time.
The specific time components of the covenant are recorded multiple times across the second half of Leviticus 26. Each time it is mentioned, lest anyone should miss it, the covenant stated national punishment for breaking the covenant would last "7 times." The following is an example of one of the references where this phrase is used:
24Then will I also walk contrary unto you, and will punish you yet seven times for your sins. (Leviticus 26:24 KJV)
24I myself will be hostile toward you and will afflict you for your sins seven times over. (Leviticus 26:24 NIV)
I will also walk contrary to you and I will punish you7 timesFS for your sins.(Leviticus 26:24 BRB)
This expression "7 times" repeats and as is typical of biblical language that repetition implies certainty.
How long does punishment run?
The expression "7 times" has a very precise chronological meaning. The word "times" typically means year, but as this is a nation entering into the covenant, not individuals, the days that compose that year are themselves 1 year long.
In this case, then, the expression "7 times" means that God will punish this nation 1 year for each day there are in 7 biblical years. As the total number of days in 7 biblical years is 2550, the total number of years in this punishment period is 2550 years.
What would God do?
The rest of Leviticus 26 explores in detail just what God would do. These details happened to ancient Israel at various points in her recorded history. One thing not mentioned, but important to this story, springs from the way God entered into covenant with Abraham.
Abraham had taken a series of animals, split them in two and had been prepared to walk between them as a sign of entering covenant with God. God, though, through his representation as a smoking fire pot had gone through the animals alone. This had made the covenant with Abraham unconditional. There was nothing binding on Abraham.
If Abraham had walked between the animals, he would himself been subject to division should he have broken the covenant. The symbolism of the split animals being this: If either party to a covenant entered into by walking between the pieces, should fail to keep their part of the bargain, the other party had the right to cut the offending party into two pieces, just like the animals.
The same "walking between the pieces" act at Sinai happened when the nation walked between the split waters of the Red Sea. The nation was subject to division, as well as the other features of the Sinai covenant, should the nation break that covenant.
That division happened at the Civil war in Rehoboam's reign and is the start of the period of punishment. We look at that in the next article.
1. S. Corinthians 3:14
2. Hebrews 8:6
3. Galatians 3:29
4. Leviticus 26:1