Officials in the Obama administration on Tuesday spoke with state budget officers about how they should respond to the federal government shutdown, but provided little insight into what will happen if it lasts more than a month.

READ: Full coverage of the federal shutdown's impact on states and localities.

For state governments, the shutdown forces them to consider whether they can afford to essentially loan money to federal programs -- and whether they consider Washington reliable enough to pay it back.

The call was led by David Agnew, head of the White House Office of Intergovernmental Affairs, and was attended by officials from several federal offices, including the Office of Management and Budget. State budget officials from across the country participated, trying to figure out how much flexibility they'll have as the federal funding spigots start to run dry.

Administration officials reiterated that several programs could continue with relatively stable funding through October. As Governing reported earlier this week, programs like Supplemental Nutrition Assistance (SNAP), school breakfast and lunch, and Women, Infants, and Children (WIC) -- for technical reasons -- could continue well into the month.

But it's unclear what happens if a shutdown lasts beyond October. "They didn't talk about anything after October," said one participant in the call, who requested anonymity because it was closed to the press. "It's triage."

Several state budget officials questioned whether the feds would reimburse states if they use their own funds to plug federal gaps. "They made it clear that's their intention, but it will be determined by the appropriations," the participant said.

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In a media event after the call, Michigan's budget director John Nixon said there were still "lots of unanswered questions." He highlighted the fact that his office has generally considered the federal government to be one of the biggest risk factors impacting the state's ability to stabilize its economy. Nixon's office has already warned state employees of the potential for federally-funded positions to be furloughed in the coming weeks.

Michigan has a rainy day fund of $580 million, and an average of about $18 million federal funds per day could dry up due to the shutdown. So while the state could cover the difference in the short term, Nixon feared the impact of state spending "without a promise to be reimbursed," emphasizing the rainy day fund is meant to cover the state's responsibilities and not those of the feds. "We will not be acting as the federal government's bank," Nixon said.

Nixon reiterated that SNAP and Temporary Assistance for Needy Families (TANF) programs shouldn't be impacted by a shutdown lasting a few weeks, and the state should be able to carry forward WIC funds for about 10 days. But, he said, "in two weeks we really start to feel the pain," and the "real problems" begin if a shutdown goes longer than a month.

In the case of food stamps, Nixon said the state could plug the gaps temporarily if there's just a cash-flow problem and an end to the shutdown is in sight. But the state can't afford to simply take over that program indefinitely.

Other states are making similar statements. North Carolina's budget director Art Pope, for example, explicitly told department heads not to increase the state funding percentage in programs that get federal funds. A lack of federal guidance, he said, meant state agencies shouldn't count on federal reimbursements.

"The issue is going to be if this becomes a protracted stalemate, beyond what we saw in 1995 and 1996," says H.D. Palmer, a spokesman for California's finance department.

In California, 1.9 million people depend on SNAP. An average of 4.5 million free meals are distributed to school children every day. If the situation drags on to November, the future of those programs becomes questionable.

Reimbursement, Palmer says, "is not something the executive branch can guarantee on its own."