In all likelihood, Sanders isn't going to get most of what he wants accomplished. Contrary to the rhetoric that happens every four years, The President isn't very powerful for reasons Justin's already mentioned. With Democrats, the cycle is especially vicious because they're sort of like the people who are huge fooball fans on Superbowl Sunday and never watch a game the rest of the year. There's probably also some discouragement over the fact that all the things that the Messiah of the moment promised during the campaign aren't happening. In any case, Democrats don't show up for the mid-terms, the Republicans take (or keep) control of Congress, and the corporate media tells us that the mid-term elections are the American public showing that they don't want Democratic policies. Achievement unlocked: Stats Quo Maintained.
To answer the original question, most of Bernie's programs are funded by raising taxes on those who make over $250K, closing off-shoring and hedge fund loopholes, and taxing Wall Street trading (which might also reign in the kind of casino gambling that caused the 2008 crash). His medical plan also pays for itself by forcing drug companies to negotiate with the federal government and implementing single-payer, which cuts out the overhead private insurers spend on advertising and CEO pay. Taxes will go up, but you won't have to pay insurance premiums if you want health care, so most households will pay less overall.
But none of that's going to happen during Bernie's term, so why vote for him? There are a couple of reasons. For one, change can happen if there's enough popular support. Many of the things Bernie proposes are popular. The problem is that there's a sort of gentleman's agreement between politicians to pretend there's not popular support. If there's a vocal movement and the President makes it clear that the Congress is the bottleneck, it can scare Congress into acting to keep their seats (or get voted out if they don't because there's enough of an uproar to convince people there's a Superbowl happening during the mid-terms). Sanders will use the bully pulpit so hard Teddy Roosevelt will come back from the dead to high five him.
Also, Sanders has said this isn't just about electing a president, it's about creating a movement. Most of the grassroots activity from a presidential campaign stops the day after the election. Sanders is trying to build machinery that will keep going after he's elected. I'm not really well-versed in the details, but apparently he's done it with his campaign machinery for lower offices, so hopefully he can repeat it here. Basically, he's playing the long game. He knows he might not get campaign reform or universal health care during his presidency, but he's trying to lay the groundwork for it to happen eventually.
And yes, Obama did make the same kind of promises only to continue Bush administration policies once he got elected, all politicians make big promises, etc. etc. The main difference is that with Obama, we were betting on a guy without much of a track record. Sanders has been pushing for the same things in different offices for decades, so I don't think he'll suddenly change his mind if he gets elected.
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