Love fired back that Matheson was using untrue attacks to distract from the real issues.
"I think Jim Matheson should be ashamed of himself," Love said. "I think for him to take these kids and try to use them for political gain, it just shows his lack of leadership and lack of ability to talk about his own record."
The exchange comes with less than two weeks left in an election that, according to recent polling data, is dead-even.
Matheson said that, since 1975, when Congress passed the Individuals with Disabilities Education Act, there has been a commitment to provide an education to special needs students and doing away with the funding would limit the opportunities for those students and put additional demands on parents.
Earlier this year, Love put out a fairly specific proposal to cut federal spending that included eliminating all federal education subsidies. A more detailed proposal by The Cato Institute, on which Love's plan was based, specifically called for eliminating special education funds.
Love has also called for elimination of the Department of Education, which allocates the IDEA funding.
But she said on Wednesday that, while she supports getting rid of waste, abuse and unnecessary bureaucracy, she would not "pull the rug out from under these children."
"I think it's important for us to do what we can to advocate spending money on a local level," she said. "I'm not going to remove that funding from those children without it being allocated on a state level, but we have to find ways to make sure that works. … I think we can do it better on a state level."
Heather Cannon, a mother of three children with autism, said during Matheson's press conference that she felt "angry" and "disgusted" at the thought of doing away with special education funding.
"Eliminating federal funding would essentially be telling the many, many families and their beautiful children that they don't matter," Cannon said.
Both campaigns appear to be targeting women voters down the stretch with Matheson's message targeting special education and Love scheduled to host a women's business forum on Thursday.
Love is also bringing in national Republican figures to try to help push her over the top. House Majority Leader Eric Cantor will headline a fundraiser for Love on Thursday and House Speaker John Boehner will make his second visit to campaign for Love on Halloween.