That's what Trump promised to do, and his supporters would chant at rallies. But lets examine the metaphor more closely.
He suggested term limits to do this. Term limits don't drain the swamp. It just changes who inhabits it every few years. It doesn't address the cause of the swamp.
In a real swamp, it's water that runs into a low lying area and stays that gives rise to the swamp that supports its inhabitants. The analogous thing in DC is the money that flows into campaigns from lobbyists, wealthy individuals and corporations. Millions of Americans want to end Citizen's United with a constitutional amendment. But Trump never said a word about placing any limits on money in politics.
Trump even bragged openly in the primary debates that he has given money to many candidates on both sides of the isle, and that when he asked for things he always got what he asked for from those he donated to. He accused Clinton of pay-for-play, and openly confessed to engaging in it. Just one of many, many examples of a "pot calling the kettle black".
So he promised to drain the swamp he helped create by changing it's inhabitants, not stopping the flow of money that creates it. Actually, a regular forced turnover of inhabitants actually gives people like him a greater chance to influence those who are there. Incumbents have the weight of being an incumbent and would be more likely to withstand the temptation to take money for favor. It’s newcomers who need money more.
Millions voted for him because he wasn't a politician, was an outside to DC, and not establishment. But he promised all kinds of things, and lied, a lot, just like politicians do. And now he's hiring all kinds of establishment (financial and governmental) insiders to work for him.
Trump really is part of the financial/economic establishment that has corrupted this country so much. So now his voters helped elect (at least via the Electoral College) someone from the financial/economic establishment to replace the governmental establishment they came to despise because the financial/economic establishment wielded an inordinate amount of power and influence.
Like he said, "We love the uneducated".