“I forget I’m talking to a 3-year-old,” Kim Webster said.

These are critical years in a child’s life, a time when achievement gaps emerge, and the prime moment to intervene. But in Massachusetts, 30,000 children from low-income families linger on preschool waiting lists, unable to obtain the state voucher that will pay for their care. The backlog has nearly doubled since 2011, when state budget problems led to a freeze in issuing new vouchers.

“We have empty seats,” said Deborah Kincade Rambo, president of Catholic Charities of Boston, which serves about 1,100 children. “We know there are people out there who would like to be able to get their children into child care, but they can’t because they can’t access the state subsidies.”

And if parents don’t have access to child care, parents can’t work. “So,” she said, “it’s a never-ending cycle.”

To begin putting more students in classrooms, Governor Deval Patrick has proposed boosting spending on early childhood education next year by about $130 million. Those dollars would be used to increase the pool of money low-income families can access to help pay for day care. It would also bump up the rate paid to day care centers. The governor also wants to increase capacity during the next four years.

Patrick’s proposed $34.8 billion budget for the fiscal year beginning in July, which calls for nearly across-the-board increases in state spending, makes it a goal to move all children toward being proficient readers by third grade. The spending increases would be paid for in large part by a $1.9 billion tax hike and a $400 million withdrawal from the state’s reserve fund.

Massachusetts early child-care educators say that Patrick’s proposal would help restore balance to a system thrown out of whack by the voucher freeze. Slots open up as children age out or move out of early child-care programs, but new children cannot enroll because their families cannot access needed subsidies, said William Eddy, executive director of the Massachusetts Association of Early Education and Care.

Fewer students mean less revenue, so providers shrink capacity to cut costs, Eddy said. The question is: Do I hire a teacher and open a classroom with only a handful of students? The answer, he said, is often no.

“The whole Massachusetts early education system is completely destabilized right now,” he said.

And, he added, it does not help that the state has failed to increase the value of vouchers for six years.

Sherri Killin, state commissioner of early education and care, said the decision to block access to vouchers was the result of an unstable economy.

“We have seen a surge of about 2,000 people per month go on to our waiting lists and we have not been able to respond to that need,” Killin said.

There is no guarantee the governor will get what he wants in early education or other state programs. Leaders in the Legislature, which must approve Patrick’s budget plan, have suggested some elements might have to be scaled back.

But should the Legislature pass the budget, child-care providers, big and small, across Massachusetts have wish lists ready. Classrooms will be reopened, retirement benefits restored, salaries increased, and training programs replicated.

Cindy Gagliastre, as director of Tiny Treasures in Worcester, has become all too familiar with the spirals of the child care funding system as she watches the enrollment of her small child-care center fluctuate. Many of her parents are struggling financially and are right on the eligibility line for vouchers, she said.

“Or,” she said, “they are on the list and the list is so long that by the time they get the voucher, they don’t have the job any more.”

Her center cares for 37 children, and six families pay using state vouchers. If more parents have access to vouchers and the vouchers pay the providers more, Gagliastre said, “we can implement some extra things that we’ve had to cut back on.”

She’s cut back on field trips and only buys necessities, and she would like to pay her staff of eight a bit more but cannot afford it.

Vouchers for preschoolers pay $150 a month less than what parents who pay out of pocket are charged at Tiny Treasures. The difference for toddlers is $100.