That's a pretty common question (about getting out of debt quickly), most Americans want the quickest results possible whether they're getting their car or their finances fixed. And while there's nothing wrong with wanting to get out of debt as fast as possible, the approaches you should take and the time it takes accordingly will vary depending on quite a few things.
How much debt do you have? Some people have a few thousand dollars they'd like to pay off, some people have tens of thousands of dollars. While as a whole the amount of time it takes to become debt free depends on a number of factors, all other things aside the more debt you have, the longer it will take.
How much income do you have? The more 'disposable' income you have, the more money there is available to pay down your debts each month. While the approach you take to eliminating your debt will effect the time things take, all other things aside the more income you have, the quicker the process will be.
If you're considering going with a debt consolidation loan, you can pay things off most quickly by securing the best interest rate, then applying all of your disposable income towards the reduced interest debt. With more money going towards the balance and less towards interest, it should be easier to take down the principle owed than it was on the original debt(s), which means you'll be debt free sooner.
Of course, getting a consolidation loan usually requires some credit, or at least a low debt-to-income ratio to secure. It also assumes you're not totally in over your head with the amount of debt that needs to be paid off. If that's not the case, you might be considering settlement as an option.
If there's no way that your income will allow you to pay down your debts, even with lowered interest rates, it's probably quickest to have a good debt arbitrator handle settling your debts for less - but that will have an effect on your credit reporting, and will make that mortgage loan much harder to get without at least a couple years in-between.
If you're concerned about your credit history (and you should be if you're looking for a home loan), don't be in too big a big hurry to pay off debt fast - in the long run a good credit score can save you lots of agony (and money the from lower interest rates you'll get).