Republican leaders said Thursday they plan to pony up $12 billion to $15 billion in the coming months to begin construction of President Donald Trump’s proposed border wall, but that large sum of money may be just the first installment to fund a project that could cost taxpayers as much as $40 billion, according to some independent estimates.

In addition, Republicans face likely opposition not just from Democrats but also centrist Republicans and fiscal hawks who would balk at seeing that kind of tab added on to the deficit. Travis Hall, a spokesman for the House Republican Study Committee, said the conservative group will insist on offsets, as it has with supplemental appropriations in the past.

And trying to take the money from other domestic accounts would provoke howls of pain from advocates for those programs, from both parties.

At a joint Republican retreat, House Speaker Paul D. Ryan of Wisconsin and Senate Majority Leader Mitch McConnell of Kentucky told reporters that they would pass a supplemental appropriations bill for the current fiscal year, which ends Sept. 30, to jump start work on the wall along the U.S.-Mexico border. Trump signed an executive order Wednesday ordering Homeland Security officials to begin drafting plans and identifying available funds for the project, as well as putting together a budget proposal to present to Congress.

A final price tag will likely remain murky until the administration hammers out final details, like what material they’ll use to construct the wall; who will build it; and what portions of the Southern border it would cover.