It depends what you mean by rush.
As the saying goes, brisket must be "cooked beyond well done and into tender." Personally, I haven't had good luck with a three step process of partially cooking; stopping, holding, refrigerating; and finishing the next day. The brisket never gets really tender. In my experience, you simply have to take it from start to the correct final temperature, 192F - 198F, in one step. I'm afraid that puts me in disagreement with some of the other posters -- but it's based on a lot of experience with all sorts of smokers -- including small offsets.
If you need a reason, a barbecue guy would say the "fats and connective tissue" won't "melt" and "baste the meat internally." The truly weird part is that it's pretty much right. You see, once they've been heated and cooled, the collagens and lipids will never denature in the same way they would have if they'd been gradually heated in a single step. More, if you partially cook to 160F, then reheat to 190F, the results will be dry. Tough and dry. Yum.
I can teach you to "master" the offset pretty easily. It's mostly a matter of inexpensive mods, a decent thermometer, and the discipline to stop looking inside the cooker. But the mods aren't happening this weekend, I guess.
Some comp smokers like to fast cook brisket. Ray Lampe for instance goes with a cook chamber temp of slightly over 300F. I have another friend, not as famous or successful, who smokes at around 325F and does a reasonable job with brisket.
I like to smoke brisket in the 270F - 280F range. It's a compromise temperature. It's hot enough to avoid the "stall" so 50 min/lb provides a reasonably predictive finish time -- but not so hot that the bark gets too tough.
All well and good. As a novice, small offset owner who probably doesn't use a charcoal basket or an Afterburner, and who probably doesn't own a decent cook chamber thermometer (the door thermometer which came with your unit doesn't count) -- you can't hold any given temperature for very long, period. Not a high temperature without getting a runaway fire.
That leaves us with "what to do." Which is where you started anyway.
Assuming you don't have a charcoal basket:
Acquire a chimney type charcoal starter if you don't already have one. Clean out the firebox completely -- rake out ALL of the ashes.. If you haven't already, make a rake by bending a flat piece of metal (aka bar stock) into an "L" shape. Use something wide enough to get the ash easily, but narrown enough to fit under the charcoal grates. Make it long enough to use comfortably when the fire is going.
Make sure the charcoal grate is in the firebox so air can get in under the coals. If your smoker came with two grates for the firebox (charcoal and a grill grate for food), lean the grill grate against the door, so there will be an airspace between the door vent and charcoal.Open the vent on the side door completely. If the vent doesn't operate properly, fix it. Close, then latch the door. Open the flue (chimney) damper completely.
Fill the firebox to within an inch of the top door or opening to the cook chamber, whichever is closer. Use a mix of hardwood lump charcoal (not briquettes!) with a few pieces of hardwood chunk mixed in (not laid on top). Open the cook chamber, remove one or two cooking grates, and put a drip pan (you can use disposable aluminum) beneath where the brisket will go. Then replace the cooking grates. You can do all of this a day or two ahead, if you like.
Note: If you use mesquite lump charcoal, you'll get enough smoke flavor on the meat so as to not actually need more lump -- that doesn't mean you can't use it if you want.
When your brisket is prepared and ready to cook:
Start a large chimney's worth of charcoal. When the charcoal is fully lit (glowing red hot on top), spread the hot coals on the charcoal in the firebox. Close the top door (the cook chamber door should be closed as well). Leave the door vent and flue damper all the way open and walk away for fifteen minutes. No checking, no peeking. Fifteen minutes.
Return to the smoker, open the top door on the firebox and check on the fire, which should be going pretty well. If it isn't, you'll need to start another chimney. Assuming it is, close the top door. Adjust the door vent so that it is only about 1/3 to 1/4 open. The flue damper should remain completely open at all times when cooking with a live charcoal and/or wood fire.
Open the cook chamber, put the brisket on the cooking grate fat side up, and close the cook chamber door. Get the door closed as quickly as possible. Resign yourself to the fact that you may not, will not and cannot open the chamber door again while the birsket is in the cooker. If you planned to mop or baste the brisket, change your plans.
Every hour (not more often), check on the fire by opening the top door. When the fire has burned two thirds down you'll need to add more charcoal/wood mix to the same level as before. This will probably take about two or three hours. The old fire should light the new fire handily -- so that you don't need to use a chimney again. Do this as quickly as possible so as to get the firebox top door closed as quickly as possible.
When you add more charcoal, open the firebox side door and check to make sure the air space under the charcoal grate isn't clogged with ash. If it is, you'll have to rake it out. Close and relatch the side door.
FWIW, following these instructions, your fire will probably have run fairly steadily in the 220F - 240F range.
After six hours for a whole brisket or three for a flat or point, the ,meat will have taken on about 90% of the smoke it possibly could. Good enough. Preheat your oven to 325F. Remove the brisket from the cook chamber, take it into the kitchen and set it on your board.
If the meat wasn't already trimmed, trim the fatcap to about 1/4". (Easy to do when it's hot.) If you can't manage a very close trim, take it all the way off. Brisket fatcap doesn't render or digest easily; and more than a 1/4 inch is both unpalatable and indigestible. Sprinkle some dry rub on the freshly trimmed brisket. Place the brisket in a roasting pan which fits it closely. Put a little moisture in the pan -- 1/4 cup of beer or wine does nicely -- and cover the pan tightly with foil. Set the pan in the oven, and cook the brisket until it's reached a 192F internal.
When the brisket is finished, drain, defat and reserve the juice at the bottom of the pan. Use it as you ordinarily would, either as a stand-alone "au jus," or to enrich the sauce for the brisket.
The brisket should be held warm for at least one hour before slicing and serving. It can be held for as long as six hours in an insulated cooler, if it's removed from the roasting pan, tightly wrapped in either foil or restaurant quality cling wrap (home wrap will melt). Two to four hours is an ideal rest. Be aware that in this case, holding is not only "resting," but a part of the cooking process allowing the proteins to continue the denaturing process.
Without knowing more about your cooker, the type of charcoal you'll be using, the size of your brisket, etc., I can't give you an estimate on cooking time. Your schedule may force you to cook the day before and reheat.
In that case, reheat the brisket in a 275F oven until it is 140F internal, slice and serve. For a full brisket, figure at least an hour. For a half, about forty five minutes.
Always carve brisket (and any other grained muscle) across the grain. Use the longest, sharpest knife you have. If you're using a full, packer cut (point and flat), separate the point and flat before carving. Their respective grains do not run in the same direction, but are about 90* out of phase. Brisket should be sliced 1/4" to 1/2" thick. Slice thinner for chewier brisket, thicker for brisket which threatens to fall apart.
Hope this helps,