(Adds comment from Rauner and Emanuel, budget details, credit agency warning)

By Karl Plume

SPRINGFIELD, Ill., May 31 (Reuters) - A standoff between Democrats who control the Illinois legislature and the state's Republican governor will extend into the summer after no deals emerged by the end of the spring legislative session on Sunday.

Democrats and Governor Bruce Rauner failed to agree on a budget compromise, leaving Illinois with a new state budget that has a revenue shortfall of at least $3 billion.

House Speaker Michael Madigan and Senate President John Cullerton, both Chicago Democrats, ordered their chambers back into session in June. Lawmakers will be in continuous session with as little as 48 hours' notice throughout the summer.

Democrats passed a $36.3 billion spending plan for the fiscal year that begins on July 1 instead of a $32 billion budget proposed by Rauner in February. Madigan acknowledged last week that the Democrats' budget has insufficient revenue.

Rauner, who vowed he would not sign an unbalanced budget, called the legislative session "stunningly disappointing."

"We're going to have a rough summer," he said, adding that he planned to continue negotiating in good faith "to get major structural reforms as part of a truly balanced budget."

While the Democrats' budget covers the state's fiscal 2016 contributions to its five pension funds, no legislation advanced to deal with Illinois' $105 billion unfunded pension liability.

The Illinois Supreme Court in May voided a 2013 cost-saving pension reform law, ruling that the state constitution provides iron-clad protection against pension cuts for public workers.

Credit-rating agencies have warned Illinois, which has the worst-funded pensions and lowest credit ratings among all states, could sink into low-investment-grade triple-B if it fails to produce a credible budget.

Rauner said he has whittled down his so-called turnaround agenda of reforms he wants the legislature to pass as part of a budget compromise that includes issues over workers' compensation, right-to-work zones and local property taxes.

Democratic leaders say the proposed reforms are bad for the middle class.

With contracts with union workers expiring soon, the legislature passed a bill requiring mediation of collective bargaining agreements between Illinois and state employees which supporters said would prevent strikes or lockouts from disrupting crucial state services.

Republican lawmakers said the bill would strip employees of the right to strike and change the rules for already-in-progress negotiations.