The part time vs. full time distinction is stupid, but then again so is this thread. You see threads like this one every once in a while, "look at how hypocritical the socialists are, they call for an end to private property but own property, they call for an end to capitalism but hold jobs in the capitalist work force, they call for increased spending on homelessness but haven't given all their money to the homeless." This is yet another example of a failure to understand the difference between systemic solutions and individual actors because the people who make these argument, are, without exception, morons.
The socialist party does in fact call for a higher minimum wage. As was already pointed out, by purchasing power, during the heyday of the US economy, this minimum wage already existed when adjusted for inflation. Clearly it was manageable, and not just manageable, it existed in a time of unprecedented economic growth. The only thing that has changed since then, really, is that shareholder expectations have gone up to the point that labor no longer counts for much in economic terms, only ownership. This has been championed by calls for deregulation by the wealthy and everyone else in the Republican party (and to be fair, much of the Democrats), hereafter referred to as "Useful Idiots". Between these groups, the protections of workers and unions have resulted in a downward standard of living relative to overall economic prosperity. That restoring the US to an economic system comparable to the 1960's passes for socialism these days is in and of itself amusing, but that is beside the point.
The point, then, is what of the 13 an hour web developer when they call for 20? Well, quite obviously, they can't afford 20. "Aha", I hear you say, useful idiot that you are, "but this proves that minimum wages cost jobs and blah blah blah blah (please just fill in the rest of your inane and already disproven elsewhere by economists and actual data gathered after actual minimum wage hikes rant to spare me the trouble of typing it)." No, wrong. What this proves is that in the modern socioeconomic climate of incredibly loosely regulated global capitalism, money concentrates at money meaning the small, independent voices tend not to have a lot and giant actors tend to have more than they can spend. As deep in the right wing bubble as the useful idiots here are, even you had to notice companies like Apple hoarding giant sums of cash because they have literally nothing else to do with it.
What the minimum wage does is it forces some of the money that otherwise goes to Swiss bank accounts, corporate rainy day funds, and investment in giant companies that have enough money anyway and are just going to pay it out in bonuses back into the economy where it would do some actual good, stimulate some growth, allow people to afford to buy houses again, consume luxury goods, etc. It is often noted (whether correctly or not), that Henry Ford (commie that he was) figured out that it is good for business when people can afford to buy what you are selling.
If you find on their site that they want a 20 per hour minimum wage, except for political parties, then you can talk about hypocrisy. Saying they want to make a systematic change that would require they and everyone else pay 20 an hour while they are only paying 13 and hour now under the current system is not hypocrisy because the proposed change would hit them too. If there a mention in the article about them continuing to pay 13 after the minimum wage hike they are proposing? No? Then if you called hypocrisy, you too are a useful idiot.
Bringing this full circle, what this not even really socialist party wants is to change the minimum wage so that, among other things, they can afford to pay 20 per hour. By raising the minimum wage, it keeps money in circulation where money is actually spent which would fuel their own coffers by raising revenue across the board by encouraging spending by the spending class, which would allow them to pay more than what they can pay now. If it turns out a minimum wage increase does not increase their funds available, and they can't afford to pay more, they they would have to do without their web developer under the letter of their own law, which, again, nothing on their site says they should be exempt from.
But perhaps I am too harsh; please, useful idiots, tell me more about how the left are hypocrites for claiming their tax refunds while thinking the rich should pay higher taxes.