COLUMBUS (AP) — Lawmakers scrambling to reach a budget deal canceled a meeting planned for Sunday, reflecting a continuing stalemate over the issue of slot machine gambling and casting serious doubt on their ability to meet a July 1 deadline.

The meeting was rescheduled for Monday, leaving almost no time for lawmakers to reach a deal that could be voted on and signed by the governor. The possibility of lawmakers having to pass a temporary budget to fund government at reduced levels for at least a few days looms heavily.

The dispute over Democratic Gov. Ted Strickland’s gambling proposal has overshadowed all other negotiations on the roughly $54 billion spending plan, which must be trimmed by $3.2 billion to account for an expected drop in revenue.

‘‘I cannot get past the fact that the voters of Ohio — our constituents — have spoken on expanded gambling time and again,’’ Senate President Bill Harris said in a statement late Saturday. ‘‘Asking the General Assembly to circumvent their will in such a short time frame when there has been no formal public debate and there are so many questions left unanswered is unreasonable.’’

Harris believes Strickland can use his executive authority to bring the slot machines to Ohio’s seven race tracks and raise an estimated $933 million for the budget. But Strickland reiterated Sunday that he needs legislative approval to put the proposal on solid legal ground and to give confidence to the gambling industry that Ohio is a safe investment.

‘‘We have heard the objections, but unfortunately still no solutions,’’ Strickland said in a statement. ‘‘I believe that the Senate majority understands the gravity of the situation before them.’’

With the Senate’s refusal to touch the gambling proposal, lawmakers will likely have to turn to erasing the budget deficit solely with cuts — all sides have said a tax increase would harm the economy further.

Strickland said it’s up to the Senate, now that it has rejected his proposal, to come up with an alternative way to cut the $933 million from the budget. In his plan, Strickland also proposed $2.4 billion in cuts.

Advocates for state services from libraries to food banks have already cried out over the cuts they would receive from Strickland’s proposal. Libraries faced a nearly 50 percent reduction in state support while food banks would see $8.5 million a year under the governor’s proposal, the same funding they were receiving before the severe recession greatly increased demand for food aid.

‘‘We’re all very, very concerned,’’ said Lisa Hamler-Fugitt, executive director of the Ohio Association of Second Harvest Foodbanks, on Sunday. ‘‘With no action thus far and the inability of leadership to come up with a revenue source it doesn’t look good.’’

Resorting to plugging the deficit solely with cuts may also have political implications for the budget’s passage. A handful of House Democrats have split with their governor to call for a tax increase, and some have said they won’t vote for a budget that only has cuts.

With only a 53-46 majority in the Ohio House, the Democrats do not have much leeway to lose votes and still pass a budget plan.