The Senate’s plan to address job creation through a series of smaller bills isn’t cutting it with some powerful House Democrats, who are renewing a push for a larger $100 billion package of aid to state and local governments.

The Senate Democrats’ piecemeal strategy has been bearing fruit — they passed a big tax extenders bill Wednesday on a 62-36 vote and are finishing up work on an earlier jobs tax credit bill, with a small-business tax credit bill yet to come.

But those measures don’t include much in the way of spending items that House Democrats and liberals have been demanding, particularly aid to prevent a wave of hundreds of thousands of layoffs of teachers, firefighters, police officers and other local workers across the country.

On Wednesday, House Education and Labor Chairman George Miller (D-Calif.) proposed a $100 billion two-year package of aid to state and local governments to try to pressure the Senate to think bigger.

Miller’s latest proposal includes some pieces of the $154 billion package the House passed late last year, but unlike that earlier package, it is focused almost exclusively on aid to state and local governments. Appearing on a conference call with mayors and Reps. Keith Ellison (D-Minn.) and Phil Hare (D-Ill.), Miller warned that the budget shortfalls and resulting layoffs at the local level threaten to undo improvements in the private sector and delay job growth.

“This is a big bill because this is a very big problem,” Miller said. “I don’t think you can nickel-and-dime this.”

Miller said he hopes that when mayors come to Washington, D.C., next week to lobby, they will help convince the Senate of the need to act. “I think they’ve got to explain to the Senate the kind of crisis that we are in,” Miller said.

Senate leaders aren’t committing to anything in particular.

“If this is something that the House considers, we will take a look at it,” said Regan Lachapelle, a spokeswoman for Senate Majority Leader Harry Reid (D-Nev.).

But she defended the Senate’s record so far. “We are continuing to work on our jobs agenda to create jobs and get the economy moving. We have already passed legislation this year that will create thousands of jobs around the country, and we will continue to do so in the coming weeks and months.”

But the Senate hasn’t yet put together anything close to the package Miller is proposing, instead choosing to split legislation into a series of proposals that are harder for Republicans to oppose.

Miller also didn’t propose a way to pay for his package, saying that would be up to House Democratic leadership. But the Education chairman and close ally to Speaker Nancy Pelosi (D-Calif.) said his preference is to add the spending to the deficit, arguing that the jobs that the bill will support will help the economy, which will in turn help the budget.

Miller also said it’s unclear whether House leaders will try to add state and local aid to the tax extenders bill or other job legislation that just passed the Senate.

Ultimately, Miller said that last year’s $787 billion stimulus package simply wasn’t large enough. More “is going to be necessary if we are going to get the recovery Americans are looking forward to,” he said.