The covenant God made with Abraham was very specific.
It was also unconditional.
The covenant God made with Israel was absolutely conditional - and it was conditional on their obedience to the law.
The New Covenant is unconditional.
Actually make sure you get that right, God in exodus 19 intended Israel to live in the same Covenant that he promised Abraham. IT was Israel not God who established a different covenant.
Paul is clear in Galatians 4 that the old covenant was the work of men:
Gal 4:22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.
Gal 4:23 But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
Gal 4:24 Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
Gal 4:25 For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.
take careful note that Paul says that the covenant on mt sinai was bondage likened to Agar. Agar was the Egyptian servant who was a slave. Abraham slept with her to bring the promise of God. But the promise of God does not need men to bring it about. Thus it was Abraham's actions with Hagar that was old covenant, not Gods promise which was new covenant.
Old covenant is not a dispensation but a reaction of the people.
Adam and Eve putting fig leaves to cover their nakedness was old covenant. God clothing them with skins and promising a messiah was new covenant.
The old and new covenant have always been around from the very beginning. They are two reactions to Gods promises.
Abraham learned the lesson and believed/Had faith in God and it was credited to him as righteousness.
But Israel when offered to enter into this same promise they said:
Exo 19:8 And all the people answered together, and said,
All that the LORD hath spoken we will do. And Moses returned the words of the people unto the LORD.
They thought God needed their help and thus God then humbles himself and meets them where they are at and gives them the law in wrath that they might see that they have made a foolish reply yet they replied:
Exo 24:7 And he took the book of the covenant, and read in the audience of the people:
and they said, All that the LORD hath said will we do, and be obedient.
They did not understand that it is impossible to please God without faith as their Father Abraham learnt. They failed to cherish the promise and accept it as it was offered. God knew this as we see here:
Deu 5:29 O that there were such an heart in them, that they would fear me, and keep all my commandments always, that it might be well with them, and with their children for ever!
God knew their hearts that without faith they were only going to stay slaves to sin and would not obey His law. He led them through the wilderness in the way He did to try an show them this very heart problem:
Deu 8:1 All the commandments which I command thee this day shall ye observe to do, that ye may live, and multiply, and go in and possess the land which the LORD sware unto your fathers.
Deu 8:2
And thou shalt remember all the way which the LORD thy God led thee these forty years in the wilderness, to humble thee, and to prove thee, to know what was in thine heart, whether thou wouldest keep his commandments, or no.
Deu 8:3 And he humbled thee, and suffered thee to hunger, and fed thee with manna, which thou knewest not, neither did thy fathers know; that he might make thee know that man doth not live by bread only, but by every word that proceedeth out of the mouth of the LORD doth man live.
But they did not get it, They after failure after failure still did not come to faith as it is written:
Deu 32:20 And he said, I will hide my face from them, I will see what their end shall be: for they are a very froward generation, children in whom is no faith.
They did not trust as Abraham did. God did not lead them into a works based covenant they rejected Gods covenant and chose to work for it which could never work. Gods desire for them then was:
Deu 10:15 Only the LORD had a delight in thy fathers to love them, and he chose their seed after them, even you above all people, as it is this day.
Deu_10:16 Circumcise therefore the foreskin of your heart, and be no more stiffnecked.
Notice again the farther was chosen, Abraham Isaac and Jacob had faith in God and this was the reason God chose them because they were the seed of Abraham in whom God had made promise. But they did not have right hearts like Abraham.
god predicts their continued rebellion based on that fact that they made a faulty covenant:
Deu 30:6 And the LORD thy God will circumcise thine heart, and the heart of thy seed, to love the LORD thy God with all thine heart, and with all thy soul, that thou mayest live.
It is the work of God to change the heart but they failed to see their need.
The problem is they rejected the covenant made with Abraham to have a covenant of works. God humbled himself and allowed it because He had promised Abraham to use his seed. But God tried to warn them constantly that unless they had faith and trusted Him they would never succeed.
Deu 4:31 (For the LORD thy God is a merciful God
he will not forsake thee, neither destroy thee, nor forget the covenant of thy fathers which he sware unto them.
Deu 5:2 The LORD our God made a covenant with us in Horeb.
Deu 5:3 The LORD made not this covenant with our fathers, but with us, even us, who are all of us here alive this day.
notice the covenant was different as I am sure you would agree.
they rejected the covenant made with Abraham and thus did not continue in it as it is written:
Heb 8:7 For if that first covenant had been faultless, then should no place have been sought for the second.
Heb 8:8
For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Heb 8:9 Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt;
because they continued not in my covenant, and I regarded them not, saith the Lord.
So it is that God gave the law to show them their need and to show them and lead them to Christ who was with them as it is written:
1Co 10:1 Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea;
1Co 10:2 And were all baptized unto Moses in the cloud and in the sea;
1Co 10:3 And did all eat the same spiritual meat;
1Co 10:4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them:
and that Rock was Christ.
God would have them look to Him for salvation not themselves.
The only reason they did not attain is not because of the law but because of the way in which they tried to covenant with God as it is written:
Rom 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
Rom 9:31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
Rom 9:32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
they did not have faith just as it says in Deut. They tried to work their way. Had they accepted the covenant made with Abraham they would not have been given the law. They would have not needed it because like Abraham they would have become the law themselves by the working of God by faith, as it is written of Abraham who did not have the law:
Gen 26:5 Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws.
how so?
Rom 2:14 For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves:
Rom 2:15 Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another
So then it is evident that the old covenant has always existed form the beginning so has the new. And the difference is how Men react to Gods promise. Some try to help God and that is old covenant. Others have faith and that is new covenant.
The difference is works vs faith. simple.
Israel chose the old covenant. God offered them the new covenant.