BY ERIN EINHORN
DAILY NEWS STAFF WRITER

Wednesday, October 24th 2007, 4:00 AM

The city teachers union dramatically expanded its influence when home day care providers voted overwhelmingly to join the United Federation of Teachers on Tuesday.

The 8,382-to-96 vote will allow the UFT to expand its membership by 20% and start negotiating with the city and state on behalf of 28,000 people who care for the children of low-income workers.

"This is important because it represents hope for us," said Tammie Miller, who cares for eight kids in her Brooklyn home. "This is an opportunity to get the respect and the wages that we deserve."

Miller charges private clients $240 a week to care for an infant, but the city and state pay $135 for the same work, she said.

The city day care workers got a boost from Gov. Spitzer in May when he signed an order granting them the right to organize. Former Gov. George Pataki vetoed a similar move last year, saying it would be too costly to taxpayers.

Critics called it a giveaway to unions looking to grow.

"Ultimately, this is going to cost everybody who uses day care more," said E.J. McMahon of the conservative Manhattan Institute.

"The last thing we need in New York is to take an informal, flexible and affordable program and to put it under the influence of a powerful public employee union, and that's what we've done in this case."