Gov. Chris Christie, New Jersey's two U.S. senators and Transportation Secretary Anthony Foxx vowed Tuesday to work together to obtain federal money for a $14 billion rail tunnel under the Hudson River -- though New York Gov. Andrew Cuomo's decision not to show up underscored the obstacles that stand in the way of the project.

Christie, Sens. Cory Booker and Bob Menendez and Foxx said in a joint statement that they had a "substantive and productive meeting" and "all of us are committed to working together on a path forward on this critical project."

The meeting was notable for the absence of Cuomo, a major stakeholder in the proposed project to build a second tunnel, add track capacity and expand New York's Penn Station. The difficulties in arranging a meeting highlight the political challenges facing the project, which experts say is vital to New York City's transportation system and Amtrak's Northeast Corridor.

Foxx wrote to Cuomo and Christie last month seeking a meeting after electrical problems in the existing 105-year-old tunnel caused delays on several days, further incensing commuters who already contend with regular backups on the nation's busiest rail corridor.

"The state of New Jersey supports the Gateway project and is committed to developing a framework with the federal government to begin it," the officials said in the statement. "We all recognize that the only way forward is equitable distribution of funding responsibility and the active participation of all parties. As commuters can attest, we cannot afford further delay."

The statement said that Christie, Booker, Menendez and Foxx would work to "obtain a substantial federal grant" for the project along with "other funding and financing options."

Cuomo said last week that he would not attend, saying a meeting to discuss the tunnel project was premature until the federal government committed to a sizeable investment. "There's no reason to meet now," he said. "They need to put their money where their mouth is."

On Tuesday, however, Cuomo's office backtracked, saying they were never invited to Tuesday's meeting, which Cuomo spokeswoman Dani Lever said was understood to be one focused on "New Jersey transportation infrastructure" and not the tunnel.

"It was our administration's understanding that this was a separate meeting" than the one called by Foxx to discuss the tunnel project, Lever said.

Last month's electrical failures, centered on 80-year-old cables likely damaged by Superstorm Sandy in 2012, reignited the debate over how to pay for a second tunnel and other improvements.

Meanwhile, rail experts and Amtrak officials say that, while a new tunnel will improve reliability, it won't suddenly double the number of trains between New Jersey and New York; the existing tunnel will be closed for repairs for a minimum of two years once a new one is built.

In addition, two new tracks will need to be added between New Jersey stations Newark and Secaucus, where two currently exist. And, perhaps more critical, New York's Penn Station needs to be expanded to accommodate the increased traffic.

Some elements of the project are already in motion. For example, environmental and design work has been completed for a replacement for the 105-year-old Portal Bridge over the Hackensack River, a regular source of delays. And regulatory approval for Amtrak to address adding capacity on the tracks and in Penn Station, a process begun in 2012, could be completed sometime next year.

The rest will be dictated by when, and how much, funding is available.