The Federal Transit Administration's approval means federal funding could be available in the city's next fiscal year, which begins in July, according to Mayor Antonio Villaraigosa's staff.
"These two projects represent tremendous job creation, mobility and environmental benefits for the Los Angeles region," Villaraigosa said. "Today, the federal government has given a strong signal that the Westside Subway and Regional Connector are likely to be supported with New Starts (federal) funding and that our aggressive timeline for 30/10 is not out of reach."
Both projects were among a dozen originally expected to completed over 30 years using money from Measure R, a half-cent sales tax approved by Los Angeles County voters in 2008.
"It's music to my ears, that sounds good," said construction worker Greg Quarles. "Only time will tell."
But this week's power shift in Congress might affect plans down the road.
"We're in limbo, there's no question about it," said LA County Supervisor Don Knabe. "It depends on how they deal with all these rule changes."
San Dimas' David Dreier is chairman of the House Rules Committee. He recently told NBCLA the plan is not dead.
Since then, House Republicans have suggested changing the procedure by which money is allocated for transportation.
"I think David Dreier and the other Republicans in the LA delegation obviously see the value in this because they're in the gridlock like everybody else is," said Councilman Bill Rosendahl.
Under Villaraigosa's 30/10 plan, the federal government will accelerate funding for some projects. If the Westside light-rail project is included, the $4.2 billion line would reach Westwood in 2022, instead of 2036.
If accelerated funding for the 1.9-mile regional connector is included, the underground line, which would be built downtown, would be completed by 2019.
In considering a route for the Westside line in October, Metro's board voted for a roughly 9-mile extension from the Wilshire-Western station to the Veterans Administration campus in West Los Angeles.
Metro officials, citing a study by the Los Angeles Economic Development Corp., said the Westside project should provide about 40,300 jobs, while the regional connector might create about 11,400.