There was a push from Nixon to do this years ago, I believe it ended because some didn't want to get rid of all other forms of welfare. I'm a big fan, myself.
A few problems that need to solved are:
1. Some big companies will feel no obligation to increase wages because people will make a minimum anyway, and a lot of the workers will feel the same way.
2. Some people just won't work. I prefer something like for every $1 you earn, you only lose 50¢ of minimum income. This also helps with #1
3. Left wing groups seem to always want to add more things to help people. A minimum income should be the right amount to basically pay for everything, including health care,
and it should stipulate no other forms of help may be offered other needs other than for catastrophic problems like disaster relief and unemployment, although unemployment could be provided as
a commercial insurance like disability.
4. The urge to work for money under the table will be far greater.
5. It should get rid of social security. This isn't really a negative, but a lot of people are under the delusion that it's not not a form of welfare.