SALT LAKE CITY — Legislative leaders are now negotiating with Gov. Gary Herbert to come up with an alternative to a bill he vetoed rather than hold an override session.

Both House and Senate leaders had said an override session was all but certain on SB229, a bill earmarking some 30 percent of future state revenues for road projects.

But it's apparently been difficult to find a day for the session before the May 9 deadline to override a veto when the two-thirds majority needed to overturn the governor's actions can be present.

So now legislative leaders are quietly talking with the governor about scaling back the size of the set aside in SB229 and possibly other changes that could be approved in a special session.

Herbert is likely to want to avoid the chance of a veto override. He faces another election next year and has already been described as "politically weak" by a tea party organizer.

"Legislators have brought proposals forward," the governor's spokeswoman, Ally Isom, said. "It doesn't change the fact that the governor vetoed the original bill."

Herbert said in a statement issued with his four vetoes from the 2011 Legislature that the earmark would mean less money for other budget needs and hamper the state's ability to cope with changing financial circumstances.

That doesn't rule out an alternative, however.

"He's always willing to discuss options and possibilities. It's nothing he's going to dig his heels in, in terms of not having a conversation," Isom said.

Still, she said, "there's not a commitment right now to any type of compromise arrangement" nor has a date for a special session been identified.

Unlike a veto override session, it's the governor who calls a special session and decides what will be on the agenda.

There is a possibility that another bill he vetoed could be added to any special session agenda, SB294. That bill would have changed the options health insurers have to offer in Utah and alter rates.

Senate President Michael Waddoups, R-Taylorsville, said Thursday there's only a 50-50 chance now that an override session will be held so he is working toward "getting a deal everyone can agree to."

Waddoups declined to discuss details of the negotiations. He said he spoke with Herbert about the override session last weekend at the Salt Lake County GOP convention.

"He wasn't happy about it, but I wouldn’t say he pressured me. He asked me why we were doing it," Waddoups said. "I told him we liked those issues and they were important."

House Minority Assistant Whip Brian King, D-Salt Lake, said because there's been friction between the governor and lawmakers, the override session was seen as an opportunity "to show everyone who's driving the bus."

King said the discussions about alternatives, however, suggest the GOP leaders aren't confident they can override the veto.

"You don't need to lose many people before you don’t have the number of votes necessary," King said. "Part of the reason they may try to negotiate their way out of it is it's foolish to call a veto override session and not be able to get your people in."