Washington (CNN) The White House released its budget proposal Thursday with just $1 billion immediately earmarked for the President's oft-promised border wall with Mexico -- a reflection of the fact that the administration doesn't yet know what it wants the wall to look like, the budget director said.

The $1 billion for the "first installment" of the wall would be accompanied by about $400 million in support like border security technology and access roads and nearly $300 million for Customs and Border Protection operations.

The administration is also asking for money to hire 20 Justice Department lawyers to bolster efforts to obtain the land to build the wall and 20 more staffers for immigration litigation. It would also add another $1.5 billion to support detention and deportations.

Office of Management and Budget Director Mick Mulvaney told reporters at a Wednesday briefing that the amount was all that the administration could spend on the border wall this year.

Early estimates of a full wall along the border have ranged from $12 billion to $21 billion, so the $1 billion in the supplemental funding package that the White House will ask Congress to pass quickly is just a small fraction of what such a wall could cost. More is also being asked for in the full budget request for 2018, though nowhere near the total amount.

But Mulvaney said that's partly because the administration is still deciding what it wants its wall to consist of.

"The next question is going to be: How many miles of wall does that build, right? We don't know the answer to that question because we haven't settled on construction types, we haven't settled on where we're going to start," he said.

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The supplemental budget request also includes $1.2 billion for Immigration and Customs Enforcement operations, largely to support increased detention and removal of undocumented immigrants.

Trump made building a "great" wall along the border a centerpiece of his presidential campaign and pledged to make Mexico pay for it. Throughout his nascent presidency, Trump has also maintained that the wall is a critical part of his immigration policy.

Of late, Trump has said he would ask Congress to pay for the wall and said Mexico would reimburse the US, though he has repeatedly declined to offer details on how he would get the Mexican government to do so when it has indicated no appetite for it.

There are also already indicators that funding a total wall could be a tough sell in Congress.

Asked recently if Mexico would pay for the wall, Senate Majority Leader Mitch McConnell, who estimated the wall could cost $15 billion, said simply: "Uh, no."

Democrats have also warned that money for a border wall would be a non-starter, even threatening to shut down government if such a provision is included in the upcoming extension of a continuing resolution of government funding that expires in April.

Other stumbling blocks could include where the money is coming from. Initial versions of the budget shared with Congress had steep cuts to the Coast Guard as one way of paying for the increased funding to border security -- which immediately drew criticism from some congressional Republicans.

As for the reports that the Coast Guard will face cuts, Mulvaney said, "that's not accurate," pointing to an overall 6% budget increase for the Department of Homeland Security. John Kelly, the head of that government agency, will have the discretion to allocate the money as he sees fit, Mulvaney said.

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DHS has already posted a notice that it will begin soliciting wall proposals. The initial request was then amended to refer to a 30-foot concrete structure -- then amended again to say DHS would collect both concrete barrier designs and other designs. The notice also makes clear that it is not intended as a "total wall solution," leaving itself further wiggle room as it conceptualizes the project.

Mulvaney explained that the initial allotment would allow DHS to test out "pilot cases" of the most effective means to cover different terrains and areas along the southern United States border, and said that overall spending for the border was not an exact figure yet.