As is typical for media on this issue, that article is highly misleading. That's the House, not DOGE, asking a committee to cut an average of $88 billion per year over the next decade. That committee in particular also has oversight over a stupidly large number of things from commerce to energy (as per their name) and everything inside which somehow even includes healthcare as well.

But it's impossible to cut mandatory programs' spending directly without a law passed which would require a super-majority in the Senate due to filibusters. On that note, consider now how critical the filibuster is. It wasn't long ago that Democrats wanted to end the filibuster to try to roughshod some voting law changes. Had that succeeded then now the Republican party on a super-narrow majority in the Senate would similarly be able to pass literally any law they want. Checks and balances are important because tomorrow will not be like today - a truth that will remain forever.

So in any case, they're going to need to carry out cuts not related to mandatory spending, or indirectly cut mandatory spending which can be done by things like reducing administrative costs, not spending millions of dollars on Politico subscriptions, and so on. But healthcare (or any other mandatory spending) cuts themselves will be impossible unless the DNC is also on board with it.