Ummm... yeah, of course they sped it up.
At the Remote Scanning Outpost Fermion a guy sees a irregularity in some objects traveling through Slipspace. He tries to match them up to any known Covenant ships but finds no match. Then he notices that if all the diagrams are put together, it makes the same shape as the Slipspace irregularity. He alerts Reach, and destroys all data in the facility killing himself in the process (i think). Then the Covenant drop out of Slipspace.
The UNSC had a bunch of Super-MACs that owned the -blam!- out of (some) of the Covenant fleet. So they sent down dropships (containing thousands of infantry, tanks, banshees, etc.) to destroy the generators powering the MACs. All the SPARTANs (except for John, Linda and James) are sent groundside to protect the generators alongside a bunch of marines. The SPARTANs ship (pelican/bird) is shot down while inside Reach's atmosphere. The SPARTANs all survive except for a few.
John, Linda and James (I'm pretty sure) go to Gamma Station where a ONI (Office of Naval Intelligence) prowler (a form of ship) is docked.
It has Nav (navigation) data that can lead the Covenant to the Sol system (our solar system). The three SPARTANs successfully destroy the data but James is lost (in space, his booster pack malfunctioned) and Linda is critically wounded. John helps Linda onto a Pelican (with Sergeant Johnson and some other marines) and flies to The Pillar of Autumn.
In the end the generators are destroyed and the Covenant comes in and glasses (they shoot super heated plasma at the planet, heating it to such a degree that it first burns, then gets "glassed") the planet except for a specific area on the planet.
A few remaining SPARTANs flee to the part where the Covenant didn't glass. CASTLE base, a ONI outpost, was under a mountain (inside the ground) was the only area spared by the Covenant. The five remaining SPARTANs (not including John and Linda) go there and meet Dr. Halsey. (the creator of the SPARTAN-II program). She reveals that she is the last human down here, and that she is going to set off a huge pile of explosives under the base when the Covenant tried to get in.
Before blowing it up, she fixes up the SPARTANs (clones some extra lungs, patches up their cuts,etc.) and gives them some new weapons and armor upgrades. Then they go bellow the base into some mining tunnels. They detonate the explosives, and escape.
After five days, Fred (I think) found a secret entrance into a Forerunner artifact. They found a crystal, but when picked up, it emitted (harmless) radioactivity that alerted the Covenant to their location. They stay low for a while, while the Covenant tries to kill them and steal the crystal.
At this time. John comes back into the system, after the events of Halo: CE, with a captured Covenant vessel (Ascendant Justice, with several marines including Johnson) and comes to the rescue, they all escape on the Ascendant Justice with the crystal.
Obviously this is a very long story and even if it was just up until the start of the CASTLE base part (which is the official Battle of Reach) it cannot happen in less than a minute. If you actually read all this, I salute you good sir (or ma'am).
~Hunter
[Edited on 06.14.2009 4:44 AM PDT]