LET THE HORSE-TRADING begin.

The MBTA says it needs between $27 million and $30 million to give low-income riders a half-off fare discount, but the House budget plan, despite throwing a record amount of money the T’s way, ponies up only $20 million.

In a $58 billion budget, the $7 million to $10 million difference isn’t a lot, but it could become a big deal if the low-income fare being championed by Gov. Maura Healey and her top transportation lieutenant, Monica Tibbits-Nutt, fails to get off the ground.

The new fare, approved by the MBTA board of directors on March 28, would offer riders between the ages of 26 and 64 who earn less than 200 percent of the federal poverty level a half-off fare on all bus, subway, commuter rail, and ferry trips.

Healey’s budget proposal for the fiscal year beginning July 1 called for financing the low-income fare using $45 million from the state’s tax surcharge on income over $1 million. The House plan would use $20 million from the same pot of money. The Senate budget proposal won’t be unveiled until May, so there’s plenty of time left to negotiate.

The MBTA refused to engage on the issue Wednesday, declining to say whether the program could launch this summer with just $20 million. “We are grateful for the House’s proposed investments in the MBTA and look forward to continued discussions about how to make this transformative low-income fares program a success,” a spokesman said.

House leaders said the funding level for the low-income fare was appropriate. Rep. Aaron Michlewitz of Boston, the House’s budget chief, said the $20 million represents a four-fold increase over the $5 million provided in this year’s budget.

When it was pointed out that the $5 million was only seed money to help set up the program – and not operating funding — Michlewitz didn’t budge. He said the House is proposing to spend a record amount on the MBTA in the coming fiscal year, with the focus on initiatives to improve safety and reliability.

“If it’s not safe and reliable, then it doesn’t matter what the means-tested fare system needs,” he said.

House Speaker Ron Mariano said the MBTA’s cost estimates for the low-income discount are only estimates. “It’s a moving target,” he said of the T’s cost projections. “They don’t know exactly how much it’s going to cost.”

The MBTA has spent several years researching a low-income fare program. The transit authority developed five-year cost projections that hinge on how many people take advantage of the fare discount and what impact the discount has on people who use the T’s paratransit service, which is called the RIDE.

Roughly half of the estimated cost of the low-income discount is attributable to the RIDE because paratransit trips cost the T so much. A RIDE trip in the T’s core service area costs $72, far more than the current $3.80 fare. If the fare is cut in half and demand for rides go up, the T’s costs could rise dramatically.

Over the objections of T staff, the MBTA approved an amendment proposed by Tibbits-Nutt, the secretary of transportation, to extend the low-income discount to rides outside the T’s core service area. T officials said that amendment boosted the cost of the low-income fare discount program by nearly $4 million.