These segments were funded out of DoD’s Couter-Drug money. No one is suing to stop that. In total, they plan to spend $2.5 billion from there - about twice as much as Congress authorized for the wall this year.
The lawsuits over the emergency declaration are to prevent the President from also spending money from the Military Construction (MILCON) accounts. The administration has said they intend to spend $3.6 billion from there. Along with about 600 million from Treasury’s asset forfeiture accounts, that would be about $8 billion for wall building this year - which would make a serious impact on illegal immigration. That’s why they are pulling out the stops to sabotage it.
The bottom line is that the law is very clear on the President’s specific power to declare an emergency unilaterally, and spend MILCON as he sees fit. No honest, competent judge would rule against it - so they will find some partisan hacks to delay it, and require an appeal to the 9th Circuit. Either the 9th or the Supreme Court will reverse it, after as much delay as the Left can inflict.
DoJ’s position is that the courts do not even have a role in emergency declarations, so the Administration might just drive ahead anyway, and dare the Congressional Democrats to start an impeachment of the President going into the election, to prevent securing our border.
NY and CA, along with other states and orgs, filed a suit in No. Ca. on 4/4/2019. https://ag.ny.gov/sites/default/files/filed_pi.pdf and their argument is that PDJT does not have the statutory authority to use the forfeiture funds and that the DOD transfer to the anti-drug funds is also illegal. Also they are arguing that NM has an argument that DHS has not exempted the NM sections as exempt from NERA. The complaint is not very long, but it is the only one that challenges the funding specifically.