Matthew 7:13,14 "Go ye in through the strait gate, because wide the gate, and broad the way that is leading to the destruction, and many are those going in through it;
how strait the gate, and compressed the way that is leading to the life, and few are those finding it!" This is as close as I can get to a literal translation into English from the Greek. My understanding of these two passages is the same as yours and Chloe's. The Gate is Jesus Christ and the path through Him leads to salvation and the other to Hell. And yes Scripture teaches that all are given the chance of Salvation but that few will choose it over the world.