The U.S. Treasury expects to pay $5.1 billion to prop up Fannie Mae FNMA, +2.51% and Freddie Mac FMCC, +1.84% in the coming year, according to budget documents released Monday.

The draw from Treasury has been long anticipated, as Congress directed the mortgage finance giants to steadily eliminate the amount of capital they held and remit the quarterly balances to Treasury.

With virtually nothing left in their coffers, the new tax law changes made the likelihood of a Treasury draw a certainty, as both enterprises took a hit from holding billions of dollars of deferred tax assets on their balance sheets. These assets include items like credits that can be used to defray tax bills in future years. Since the corporate tax rate has been cut, the value of those assets tumbles.

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But this is the first time a dollar figure has been given to the amount taxpayers will have to pay.

Congress originally intended the zero-capital directive as a self-inducement. The threat of a “taxpayer bailout” for large entities that confuse most Americans was seen as so ominous, legislators believed it would force them into taking action to overhaul the housing finance system.

But as that zero hour drew nearer and Congress proved unable to come to an agreement, Fannie and Freddie's regulator began to speak with increasing urgency about the need to implement reforms.

Read:Fannie and Freddie are nearly out of money and Washington is getting anxious

Mel Watt, the head of the Federal Housing Finance Agency, told lawmakers that more certainty was necessary, not just to avoid a taxpayer draw, but also to ensure the smooth functioning of financial markets.

Fannie is scheduled to report fourth-quarter and full-year earnings on Wednesday, and Freddie on Thursday. A budget appendix shows that Treasury is budgeting a payment of $4.7 billion for Fannie, which is much more exposed to the deferred tax assets, and $400 million for Freddie.

A December agreement between the Treasury Department and FHFA allowed the enterprises to keep a slim capital buffer, a step both parties said could help buy time for Congress to reach an agreement on next steps.

The White House budget also forecasts increasing the fees charged by the two enterprises on mortgages they guarantee.