By GARY D. ROBERTSONRALEIGH, N.C. (AP) â¿¿ North Carolina lawmakers cleared one more hurdle Tuesday in their attempt to overhaul the state's unemployment insurance system with a bill that would require higher taxes for business but reduce maximum weekly benefits for unemployed workers by one-third to $350. The House voted 77-42 in favor of the bill that eliminates more quickly nearly $2.6 billion the state owes the federal government for jobless claims and generates a $2 billion cushion for the next recession. The margin for the final House vote was similar to Monday night's preliminary vote, largely following party lines in favor of Republicans setting the bill on the fast track early in this year's session. The measure now heads to the Senate, where the finance committee was expected to discuss it Wednesday afternoon. It could reach the Senate floor for the first of two required votes Thursday or early next week, said Sen. Bob Rucho, R-Mecklenburg, a finance committee co-chairman. Republican Gov. Pat McCrory said he supports the bill, too, as a way to fix what he calls a broken unemployment insurance system. The bill was penned with much input from groups representing business that incurred the debt. The maximum number of benefit weeks would fall from the current 26 weeks to 20, and as few as 12 weeks in periods of low unemployment. Several Democratic House members said the bill would hurt jobless workers and put them in even further dire financial straits. Republicans who back the measure turned back two more amendments Tuesday after defeating six others Monday. "We have tried from my side of the aisle to suggest many, many things that in some form or fashion would help make that blow less devastating," said Rep. Kelly Alexander, D-Mecklenburg. Most "good cause" exceptions to receive benefits even when a person leaves their job voluntarily also would be deleted. An amendment Tuesday by Rep. Rick Glazier, D-Cumberland, that failed would have restored exceptions for workers who must care for a sick family member or can't work particular shifts because they are unable to find child care or elder care.