When I was living in Massachusetts, the pastor of my church was doing a series entitled "Crossing the Jordan." He said that a lot of hymns and spirituals treat the Promised Land as a symbol for heaven. For him, that cannot be the case, for the Israelites did not experience bliss after they crossed the Jordan. Rather, they encountered enemies and battles. For my pastor, the Promised Land is a symbol for Christian sanctification, which includes the struggle against sin.
Incidentally, in my weekly quiet time on the Book of Joshua, I found that Chuck Missler said the same thing. I'm not sure if I agree with my pastor and Chuck Missler on this point. My reason is that the Promised Land is often presented as a place of rest, happiness, and prosperity. Sure, the Israelites had to fight to possess it, but they eventually had rest from all of their enemies (Joshua 21:44). So I can easily see the Promised Land as a symbol for the bliss of heaven, or (for Armstrongites who don't believe people go to heaven) wherever the saints will receive their future reward.
When I read Hebrews 3-4, however, I get more confused. What is the "rest" of Hebrews 3-4? Is it heaven, or is it a spiritual state that the saints can possess in this life? I can see the author of Hebrews 3-4 meaning something like the following: "You must keep having faith, or you will miss out on your heavenly reward, as the Israelites under Moses missed out on the Promised Land through their unbelief." After all, Hebrews 11 emphasizes the Old Testament saints' desire for a heavenly country (see vv 14-16), so heaven is in the author's thoughts.
At the same time, there are verses that seem to present the rest as a current spiritual reality. For example, Hebrews 4:10-11 says, "For he that is entered into his rest, he also hath ceased from his own works, as God did from his. Let us labour therefore to enter into that rest, lest any man fall after the same example of unbelief." So the rest seems to be a present state of cessation from work. Christians have used other New Testament writings in their attempts to elucidate what this means. They refer to Jesus' promise of inner rest for all who come to him (Matthew 11:28-30), or they cite the Pauline doctrine that people become righteous by faith, apart from works (Romans 4:5; Ephesians 2:8-6).
But I have problems with this approach. For one, I wonder if we should use Matthew and Paul to understand Hebrews. As much as possible, I think that we should allow Hebrews to speak with its own voice. Second, Hebrews 4:11 exhorts Christians to labor for their rest. The rest that Jesus and Paul discuss, by contrast, appears to be a free gift that Christians already possess.
I guess the way that I reconcile all of this is to say that rest takes work. The author of Hebrews is writing to Christians, and yet he still sees a need to exhort and encourage them. Hebrews 10:22 says, "Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water." The author of Hebrews wants his audience to set their minds at rest by focusing on their Heavenly Father and their faithful High Priest, Jesus Christ (Hebrews 5-7; 12:2, 5-8). This takes work, especially when they're enduring persecution and the temptation to abandon their faith (Hebrews 12:2).
And maybe the hope of a heavenly reward plays a role in their current spiritual rest, since that gives them something to anticipate. The author of Hebrews may use "rest" to mean both heaven and the present spiritual peace of the saints. He wants his audience to maintain their faith as they endure this life, but he also wants them to receive their ultimate reward.