How do you suppose welfare inflates wages? Do you honestly believe the truck driving company cited is going to increase wages to attract welfare recipients? I can, with little doubt, say that they won't. Besides which, we never established how much that trucking company was paying. All we established was that you didn't want to take all of that on when you could get free money from the government.
As stated earlier, the minimum wage provides an absolute floor for wages. So that is taken care of. As far as whether or not a job is worth taking, it depends on how badly you need the money that job offers. If said trucking company is offering a decent wage for a pain in the *** job, and you have people choosing to take money from the system rather than take that job (and pay money back into the system), then your system is broken. It's not as difficult as you make it out to be. Though I suspect you know this, you just can't admit defeat.
Put a meaningful time limit on welfare, and make the time limit on unemployment meaningful. Require real verification that people receiving aid are taking meaningful steps to look for work and/or get an education. I personally know of someone who just finished drawing a year's worth of unemployment, and that person didn't want a job. They wanted to retire, they just wanted a year's worth of unemployment first. If you care anything about the burden on taxpayers, as you said you do, fix that garbage first. Force more people into the job market, where they pay into the system and help the greater good, rather than draining from it. I counted 8 Help Wanted signs on the way into work this morning. If there is a job available in a given region where there is someone on assistance, that job should be filled immediately. Not passed over because "I don't want to take all of that on."
The beautiful part of that plan is that it gives you what you always want - more money for the government (more wage earners paying taxes, less people taking money from the coffers), and more government jobs (increased staff for increased scrutiny). The problem, of course, is that liberals don't REALLY want that plan, because they can't sell it their constituents who receive assistance. So they hide behind the "We won't take money from the poor, because we're not heartless" argument. Which is complete crap, obviously.