It's a difficult question to answer, for a few different reasons.

1. If you consider absolute populations, Jews were a minority, non- Jews were a majority. So if Christianity spread among non-Jews even at an equal rate to its spread among Jews, the Gentile population of Christianity would eventually outstrip the Jewish population.

2. After the Jewish Roman War (66-70), the temple was destroyed, and Jerusalem badly damaged. Judaism took a significant turn because of this, while at the same time many Jewish-background Christians had fled from Jerusalem. This was further complicated by the fallout from the Bar Kochba rebellion (132-6), which essentially caused Judea to cease to operate as a Jewish client state and dispersed Jews from their homeland. This makes it much more difficult to trace continuities of groups of Jewish-background Christians.

3. Growing tensions between (Gentile) Christians and Jews lead to growing differentiation; you can see a discussion of this issue over in this recent thread. What this meant was that it became increasingly difficult for Jewish-background believers to maintain 'dual identity' as Jews and Christians.

4. Related to point 3, Jewish groups such as the Nazoreans, Ebionites, etc., were often regarded as heretical by mainstream Roman/Gentile Christians (Epiphanius is a good example of this). Eventually (the 2nd Council of Nicaea (787), canon 8, ruled that Jews who converted must abandon Jewish customs. This, as far as Roman and Byzantine churches went, definitively ended the possibility of existing as a "Jewish-Christian".

5. Simply tracing ancient demographic data is a difficult endeavour.

So, this is a long, round-about way of pointing out that it's a difficult question to answer, about how successful Christianity was within its early Jewish context. Modern Jews are, however, the continuation of Judaism that do not accept Jesus as the Messiah.

Attempt at clarification: Are today's Jews the few that didn't believe in Christianity or did the majority of Jews always reject it.

There were significant numbers of Jews. One of the early conflicts in the church was between those Jewish Christians who believed that all Christians must obey the Law (including circumcision), and those who took Paul's position that Christians are not bound by the Law, and in fact must not consider themselves bound by it as this would deny the sacrifice of Christ. The first group (a subset of the Jewish converts) were known as Ebionites, although it's not clear whether they were a single group. The name apparently means "the poor ones" in Aramaic.

You can see traces of this conflict in the NT. The Ebionites only used a gospel written by Matthew in Hebrew (which we call the "Gospel of the Hebrews", appropriately enough). We have fragments of this. Apparently it was generally regarded as reliable, but probably excluded from the NT as it was not in Greek. It is likely that the Greek gospel of Matthew that we have is derived from it, but this has not been established for certain.

Why does that matter? Well, if you read the Sermon on the Mount in that gospel (Mttw 5-7), and get past the Beatitudes ("Blessed are the peacemakers" etc.), you come to a part which appears to reflect a very different view from Paul:

Do not suppose that I have come to abolish the Law and the prophets; I did not come to abolish, but to complete. Truly I tell you, so long as heaven and earth endure, not a letter, not a dot, will disappear from the law until all that must happen has happened. Anyone therefore who sets aside even the least of the law’s commands and teaches others to do the same will have the lowest place in the kingdom of Heaven, whereas anyone who keeps the law and teaches others to do so will rank high in the kingdom of heaven. I tell you, unless you show yourselves far better than the scribes and the Pharisees, you can never enter the kingdom of heaven.

That part isn't in the other synoptic gospels. There's also a lot in there about specific laws which must be observed more scrupulously than was required in the OT. Overall, it seems to represent the reported views of the Ebionite community. It's interesting to note that at this period, both the Pauline and Judaising writers seem to make some effort at accommodation. So in the above, the implication is that the Paulines will "have the lowest place in the kingdom of heaven", but not be cast out. Paul similarly said that the Judaisers were Christian, even if utterly wrong. However this effort at conciliation did not last, and eventually there was some persecution of the Ebionites in Palestine. Apparently they fled to southern Arabia (I don't have a good source for that). It has been suggested that they were still going by the time Mohammed arrived, and caused the legalistic character of Islam, but as far as I know that is conjecture.

The Ebionites were only a part of the Jewish converts, but appear to have been a major part of Christianity in the earliest days. Paul's letters show a major concern with writing to contradict their preachers who turned up at congregations which he had started in Asia Minor and Greece.

If you are interested in the Ebionites, there's a podcast by Philip A. Harland "Religions of the Ancient Mediterranean", and I think you need episodes 3.7 and 3.8. His podcast doesn't overlap much with what I've described as it deals with Ebionite documents in a slightly later and more adversarial period. Interestingly, one of them describes a six year conversion process. Unless you were a Jew or had gone through this process, you were not allowed access to the teaching documents. This, and the requirement for circumcision, might explain why the Pauline strand outstripped the Ebionites. I don't think that you can just say "there were more gentiles than Jews in the empire" as an explanation, as the early missionaries went to Jewish congregations outside Judaea.