Here is an extended excerpt from the book Christianity and Liberalism, in which J. Gresham Machen highlights what was and is at the heart of this doctrinal struggle:
But what was the difference between the teaching of Paul and the teaching of the Judaizers ? What was it that gave rise to the stupendous polemic of the Epistle to the Galatians? To the modern Church the difference would have seemed to be a mere theological subtlety. About many things the Judaizers were in perfect agreement with Paul. The Judaizers believed that Jesus was the Messiah; there is not a shadow of evidence that they objected to Paul's lofty view of the person of Christ. Without the slightest doubt, they believed that Jesus had really risen from the dead. They believed, moreover, that faith in Christ was necessary to salvation. But the trouble was, they believed that something else was also necessary; they believed that what Christ had done needed to be pieced out by the believer's own effort to keep the Law. From the modern point of view the difference would have seemed to be very slight. Paul as well as the Judaizers believed that the keeping of the law of God, in its deepest import, is inseparably connected with faith. The difference concerned only the logical--not even, perhaps, the temporal--order of three steps. Paul said that a man (1) first believes on Christ, (2) then is justified before God, (3) then immediately proceeds to keep God's law. The Judaizers said that a man (1) believes on Christ and (2) keeps the law of God the best he can, and then (3) is justified. The difference would seem to modern "practical" Christians to be a highly subtle and intangible matter, hardly worthy of consideration at all in view of the large measure of agreement in the practical realm. What a splendid cleaning up of the Gentile cities it would have been if the Judaizers had succeeded in extending to those cities the observance of the Mosaic law, even including the unfortunate ceremonial observances! Surely Paul ought to have made common cause with teachers who were so nearly in agreement with him; surely he ought to have applied to them the great principle of Christian unity.
As a matter of fact, however, Paul did nothing of the kind; and only because he (and others) did nothing of the kind does the Christian Church exist today. Paul saw very clearly that the differences between the Judaizers and himself was the differences between two entirely distinct types of religion; it was the differences between a religion of merit and a religion of grace. If Christ provides only a part of our salvation, leaving us to provide the rest, then we are still hopeless under the load of sin. For no matter how small the gap which must be bridged before salvation can be attained, the awakened conscience sees clearly that our wretched attempt at goodness is insufficient even to bridge that gap. The guilty soul enters again into the hopeless reckoning with God, to determine whether we have really done our part. And thus we groan again under the old bondage of the law. Such an attempt to piece out the work of Christ by our own merit, Paul saw clearly, is the very essence of unbelief; Christ will do everything or nothing, and the only hope is to throw ourselves unreservedly on His mercy and trust Him for all.