It is possible to believe in Jesus for eternal life (and of course, receive eternal life as a result), but still not be “saved” from many of the temporal and physical consequences of sin, or from sickness, or from enemies, or from many of the other negative things that can happen in life.
We receive eternal life, not be believing the entire gospel (this is impossible anyway), but by believing in Jesus for eternal life. Though one does not need to believe the entire gospel to receive eternal life (and nobody can believe all of it anyway), one of the central truths at the heart of the gospel which must be believed is the truth about God’s absolutely free offer of eternal life through Jesus Christ.
Some Calvinists say that Calvinism is the gospel. I say that Jesus is the gospel. There are no four laws, five points, or six steps to the gospel. There is only Jesus. When a person is presenting “the gospel” they obviously cannot share everything, and so they do their best (along with the help of the Holy Spirit) to pick and choose which truths of the gospel should be shared in that particular context to those particular people.
You don’t have to believe the entire gospel to receive eternal life. This is because the gospel is a lot more than what people think. So much more, it is impossible to believe the entire gospel. Since the gospel is everything related to the person and work of Jesus Christ – EVERYTHING – it is impossible to know or believe the entire gospel. Thankfully, eternal life depends only on believing in Jesus.