Governors Chris Christie of New Jersey and Andrew Cuomo of New York sent a letter to President Barack Obama today with an offer: If the federal government picks up half the tab of building a new $20 billion Hudson River rail tunnel, the two states will split the rest [PDF].

It’s a step forward in negotiations as the governors try to secure grants from the federal government, which so far has only offered low-interest loans for the project. Ultimately, the Republican-controlled Congress must sign off on any federal funds for the rail tunnel.

The governors are also asking for expedited planning and environmental approvals, similar to how the Obama administration fast-tracked the Tappan Zee Bridge replacement.

In the letter, Christie and Cuomo peg the total cost of a rail tunnel at $20 billion. Numbers thrown around by agencies and officials have ranged from $14 billion to $25 billion, depending on the source and whether it includes related projects, like adding additional tracks from the tunnel to Newark.

The governors also said the Port Authority of New York and New Jersey, which they jointly control, “is prepared to take the lead in this effort” with dedicated staff and “an entity within the Port Authority” to involve other agencies.

The governors say this is in line with a recommendation by Senator Charles Schumer, but it’s actually not: Last month, Schumer backed the creation of a separate development corporation comprised of Amtrak, the federal government, the MTA, the Port Authority and the states to handle the tunnel project.

If the federal government takes the offer the governors laid out today, it would look quite different than the ARC Tunnel, which was budgeted at $8.7 billion in 2011, or $9.2 billion in today’s inflation-adjusted dollars. Federal funding would have paid for a third of that project, with another third coming from the bi-state Port Authority and the final third from New Jersey.

Ultimately, Christie canceled that project, then used New Jersey’s funding to prop up highway work while maintaining one of the nation’s lowest gas taxes.