State and local governments frequently find themselves on the same side of an issue when they make a pitch to federal lawmakers, and it's not unusual for members of the "Big Seven" -- the D.C. associations representing state and local governments -- to take joint positions.

But the ongoing debate over Medicaid flexibility has pitted states and counties squarely against each another in a highly partisan debate playing out on Capitol Hill.

States and the organizations that represent them back a Republican push to lift the Medicaid maintenance-of-effort (MOE) rules, which they say prohibit states from having more "flexibility" in their Medicaid programs. States are seeking the ability to impose more stringent eligibility requirements than currently allowed, which would result in fewer patients and less costs.

The National Conference of State Legislators (NCSL) has endorsed a proposal by Sen. Orrin Hatch (R-Utah) and Rep. Phil Gingrey (R-Ga.) that would remove those MOE restrictions.

But county leaders say that in many instances, counties are ultimately responsible for providing health care to the indigent. If states get what they want, the costs would just be passed along to local governments, which are facing similar financial struggles.

"Our mantra is, when states talk about 'flexibility,' that's flexibility to let someone else pay for it," says Paul Beddoe, associate legislative director for health and the National Association of Counties. "And we're going to be that somebody else."

NCSL argues that Congress should either lift those MOE requirements or provide permanent assistance to states to help accommodate the growing number of patients in Medicaid. States argue that, as the economy falters, more people are becoming eligible for Medicaid. Those same economic factors have reduced state revenue. As a result, Medicaid is using up a growing portion of state revenue (21.8 percent last year), resulting in less funds available for education and infrastructure, among other things. They say that Congress should lift the rules since the only way states can solve their budget woes is if they're able to make cuts to their largest source of spending: Medicaid.

In 2009, the federal stimulus law created new standards that required states to maintain their Medicaid eligibility requirements trough 2011. The health reform law extended that provision to 2014, when state-based health insurance exchanges would become functional (the date for children is further away). States had little choice in the matter, since they could only receive much-needed supplemental federal funding for Medicaid if they accepted the MOE terms.

But counties are vehemently opposed to lifting the MOE rules. That's because in 23 states, counties are responsible for providing medical services to low-income and chronically ill residents, and in an additional nine states, counties have limited responsibility for indigent healthcare. If MOE requirements are eliminated, hundreds of thousands of people would become uninsured -- earning too much to qualify for Medicaid but too little to afford their own coverage. In many cases, counties would have to pick up the slack.

The Congressional Budge Office says that if the MOE restrictions are pulled, then in 2013 alone 400,000 people would be forced from Medicaid and CHIPs. Of that total, 300,000 would remain uninsured. The majority of those affected would be children.

"They're going to seek care elsewhere, and in a lot of cases, the place they're going to seek care is the county," Beddoe says.

Counties also oppose plans that would transform Medicaid into a block grant program, since doing so would also decrease the number of people eligible for the program. The House GOP's budget, crafted by Rep. Paul Ryan, does exactly that. That legislation will likely be defeated in the Senate this week.

The dynamic has created two alignments: states are pinning their hopes on congressional Republicans, while counties are working with congressional Democrats. County officials, for example, joined six Democratic senators plus independent Sen. Bernard Sanders earlier this month for an event to show opposition to the block grants.

Beddoe says that the dialogue on the issue has been between the state and federal leaders, and between counties and federal leaders, but states and counties are generally not addressing the issue with one another directly.

"We love working with the states," Beddoe says. "On some of this stuff we just know we're not going to see eye to eye."