What stops the federal government from simply ignoring the vote?

Self-interest, mostly, backed by international pressure and the plain illegitimacy of stonewalling a peaceful, democratic vote. Washington could try to ignore a yes. It would gain nothing and lose a great deal, and that is exactly why the practical course for Washington is to come to the table.

Ignoring it is the worst option for Washington, not the easiest

Economies hate disruption, and a refusal to recognize a clear vote creates nothing but disruption. The settled, profitable move is a negotiated separation that keeps trade flowing and the border calm. Pretending the result did not happen freezes investment, rattles markets, and solves no problem for the federal government. When Washington has faced this kind of choice before, with Brexit, it threatened consequences, the British voted to leave anyway, and Washington promptly sat down to negotiate a trade deal. Faced with the practical path or the spiteful one, governments take the practical path.

The world is watching, and recognition is leverage

Independence does not depend on Washington alone. A peaceful, lawful referendum carries weight with the entire community of nations, and recognition by key governments and major institutions is what makes a new state real. The United States has spent decades championing self-determination and signing agreements that affirm it. Refusing to honor a free vote in Texas would isolate Washington internationally and brand it a hypocrite on the very principle it preaches. That reputational cost is real, and it pushes hard toward recognition.

Texas keeps functioning regardless

A nation exists when it governs, trades, and conducts its own affairs, and the world deals with it accordingly. Texas already runs a full government, the world's eighth-largest economy, its own power grid, and a state-level counterpart to nearly every federal department. A Texas that is up and operating is a Texas other countries do business with, whether or not Washington has sent a formal letter. Recognition does not have to be unanimous or instant to be real. Holdouts cannot un-make a functioning country.

Force is off the table, so stalling is the only card left, and it is weak

The one thing Washington cannot credibly do is use force against millions of Texans whose only act was voting, and that case is made in full in our answer on the military. With force ruled out, "ignoring it" is the strongest move opponents have, and it is not strong. Delay does not change the result. It only postpones the settlement and piles costs on the side doing the delaying. Time is on the side of the people who voted.

The bottom line

Washington cannot make a clear vote disappear by looking away. The economics, the world's eyes, and Texas's own functioning all push toward recognition and a deal. Ignoring the vote is not a strategy. It is a stall, and stalls lose.