By Dave McKinney and Karen Pierog

CHICAGO, Jan 24 (Reuters) - So severe is Illinois' self-inflicted financial ruin that its newest hope to end a record-setting budget impasse rests with a massive bundling of billions of dollars in tax increases, borrowing and pension relief for Chicago's cash-strapped schools.

The nation's fifth-largest state has been engulfed in political feuding between its Republican governor and Democratic-led legislature for nearly 19 months, making Illinois the only state ever to have gone more than a year without a full operating budget.

The bipartisan budget omnibus, which faces significant political hurdles, would raise income taxes by a third, borrow $7 billion to winnow down a record-setting pile of unpaid bills and open Chicago for the first time to legalized casino gambling.

It also would address the state's $130 billion pension crisis, change how workers are compensated for on-the-job injuries and impose term limits on legislative leaders.

Fitch Ratings has warned that failure to pass a comprehensive budget solution this month will result in yet another downgrade of Illinois' credit ratings, already the lowest among the 50 states. The state's ratings have been cut five times under Governor Bruce Rauner.

Devised by Democratic Senate President John Cullerton and Senate Republican Leader Christine Radogno, the proposal represents a rare glimmer of political détente in a state that has mostly known fiscal gridlock since Rauner took office in 2015. The plan faces its first legislative test Tuesday.

AN ALL-OR-NOTHING TACTIC

What is novel about the plan - and what also might doom it - is how it has been negotiated only between Cullerton and Radogno, leaving the feuding antagonists, Rauner and Democratic House Speaker Michael Madigan, on the sidelines.

"It's been an embarrassment that we don't have a budget, and we're the only state in the nation that doesn't have a balanced full budget," Cullerton said in an interview. "We're doing this in the Senate first because this is where we have the ability to do it on our own."

Madigan could block legislation in the House if he finds something objectionable. If the legislation does get through both chambers, Rauner could veto the package if it is not to his liking. Both are risks the plan's sponsors say they are willing to take.

The first test for Cullerton and Radogno could come in votes this week as legislative hearings begin Tuesday, with the pair employing an all-or-nothing parliamentary device in the 13-bill package. In a tactic referred to as "tie-barring," they have inserted language in each bill stating that if any one piece fails, the whole package dies.

One expert called the unorthodox and rarely employed strategy a necessity borne by Illinois' historic financial morass.

"We've never been in this position before," said Christopher Mooney, a University of Illinois political scientist. "The building is burning around us, basically. In those crisis situations, we think of doing things we wouldn't otherwise do."

The package would raise individual income tax rates from 3.75 percent to 4.95 percent, and the tax rate for corporations would grow from 5.25 percent to 7 percent. It also would authorize $7 billion in borrowing over seven years to pay down the state's $11.2 billion unpaid bill pile.

Another major component of the bill would address Illinois' $130 billion unfunded pension liability. Workers would have to choose between having future salary increases count toward their pensions or forfeit annual, compounding 3 percent annuity increases in retirement. The approach already has been labeled unconstitutional by Illinois' largest public labor union.

Additionally, the legislation would put the state on the hook for an annual chunk of Chicago Public Schools' teacher pension payments starting with $215 million this fiscal year.

Rauner's budget office last week determined the whole package would result in a $4.3 billion deficit in fiscal 2017, which ends June 30, and a $2.3 billion hole in the fiscal 2018 budget.

The governor, who has not endorsed the plan, last week expressed optimism about the package but warned it was not fully baked.

Madigan has said nothing, raising questions about his intentions. A spokesman did not respond to a request for comment on Monday.

Fitch has warned that inaction on the budget front would result in a downgrade by the end of this month.

"If they do not do something that comprehensively addresses their budget problem and their long-term accumulated budgetary liabilities, then we certainly would take action," Fitch analyst Karen Krop said Monday.

(Reporting by Karen Pierog and Dave McKinney; Editing by Leslie Adler)