I never ask for a budget. I listen to what they are asking for, discuss various ways to get it done, pay attention to how they react to certain things that might clue me in, and then design what matches our discussions.
.... then it gets priced. Sometimes we adjust the design, but not usually.
The second to last thing that I want to do is disappoint on a design because I have to cut out things that they want in order to fit the budget.
The very last thing that I want to do is crunch numbers while I'm designing.
There is a reason the car salesman has you test drive a car. It is no different than landscape design. If you show them what they really want, they often find a way to buy it. That "how to get a budget" is an extremely basic sales tool that only gets you to settle for their pre-determined number. You really are not affecting the client, only limiting yourself.
Develop your sales skills to excite the client about getting what they want, show it to them, show them what it costs, and leave them with the decision to cut things out or find a way to pay for it. You'll always be the good guy and you'll upsell a hell of a lot of projects over any budget you get out of them ..... not to mention saving the hassle of designing to a price.
When you make a landscape seem like a bunch of stuff coming out of a box and your role being the guy that will deliver the boxes you leave them with the feeling that anyone can deliver the boxes. That makes you easily replacible by the guy with cheaper boxes.
Take it to the next level by making the landscape theirs. Get everything they want into the design, show how it fits their lifestyle, the layout of their house, and how all the activities are in appropriate relations to what is going on around them. Then price it. If it costs too much, you telll them how money can be saved and let them make those decisions with you. They almost always keep it all, unless you added crap that they never wanted and you never discussed with them. This makes you very important to them as the facilitator of their design and they don't usually have the confidence that bringing in someone new will get them the same results - it is your job to lose.