* Briefing set for lobbyists with insurance a focus

* Lobbyists unsure if details to be forthcoming

* Sweeping reforms package expected mid-June (Recasts with details on lobbyist briefing, background)

By Kevin Drawbaugh

WASHINGTON, June 4 (Reuters) - The Obama administration stepped up its push for tougher bank and financial firm rules on Thursday, scheduling a briefing for lobbyists, with a focus on insurance oversight, and sending a top regulator to a Senate hearing to discuss plans for regulating derivatives markets.

The briefing, expected later on Thursday, was the latest in a series. Some lobbyists expected generalities and trial balloons, but others said it could produce more specifics, possibly widening beyond a narrow focus on insurance regulation.

"It feels to me like a bit of a roll-out activity, so I'm assuming we'll get a little more information," said Leigh Ann Pusey, president of the American Insurance Association.

President Barack Obama wants to enact new laws by the end of the year aimed at preventing a recurrence of the severe financial crisis now hammering economies worldwide.

Congressional Democrats largely share that objective, although progress toward it was expected to be much swifter in the House of Representatives, where Democrats are in firm control, than in the Senate where they are less dominant.