THE House of Representatives this week is expected to pass a federal stimulus package that could pump at least $17 billion of noncapital funding directly into New York’s state and local government coffers over the next two years. But what Sen. Charles Schumer is touting as a “shot in the arm” for New York looks more like a sock in the face to the state’s taxpayers.

The stimulus bills would temporarily offset Gov. Paterson’s planned cuts in Albany’s projected spending on education and Medicaid—the operative word here being “temporarily,” since the extra cash is only for 2009 and 2010.

As a result, the federal bailout will do painfully little to forestall the massive tax hikes now being cooked up in Albany and City Hall. Nor will it do much to “stimulate” New York’s economy (unless, like Schumer and too many other leading New York politicians, you pretend public-sector unions and Medicaid providers are engines of economic growth).

By delaying any serious reform or restructuring of New York’s most costly programs, the “stimulus” would actually make the state’s long-term financial outlook even worse. If the current versions of the stimulus bills become law, bond-raters might as well downgrade New York’s paper right away—because when two years are up, the state budget hole will probably be as big as ever, and the economic outlook may not be much brighter.

Give or take a few billion (and who’s really counting, at this point?) the $825 billion package includes $270 billion over the next two years for federal tax cuts, nearly half of which would fund the kind of targeted income-tax credits and rebates President Obama campaigned on.

Beyond that, for all the talk of job-creating infrastructure investments, the bill earmarks just $40 billion for highway and mass transit—which won’t go very far (or fast) nationwide. Roughly $200 billion more is scattered across a vast array of pet programs. Housing subsidies, college loans, energy “investments,” after-school snacks, coupons for digital TV converters—you name it, and chances are there’s a stimulus dollar dedicated to it.

The part of the stimulus package that’s really grabbing the attention of state officials is a 2½-year, $87 billion increase in the Federal Medicaid Assistance Percentage, or FMAP. New York’s share of this will come to at least $9 billion—and perhaps as much as $11 billion, if local unemployment rises even higher than now projected. Nearly a third of that money will flow directly to New York City and to county governments, which can use it to make up for shortfalls in their own rapidly plummeting sales-tax revenues.

The state’s own FMAP share should come to a little over $3 billion a year—which happens to nearly equal the amount of general-fund budget “savings” Paterson is seeking in Medicaid cuts and fee increases. Hospitals and health-care unions are already leaning on the governor and Legislature to spend all that cash to preserve the Medicaid status quo.

At least the bailout technically lets states use FMAP funds to create some maneuvering room in tight budgets. The same can’t be said for the roughly $120 billion in “stimulus” for K-12 schools and higher education. House Democrats have rigged the bill’s language to ensure that most of the money flows straight to local school districts and public colleges, where it can insulate unionized teachers and faculty members from the chill winds of a global recession.

Through various formulas, the bill looks to drive roughly $7 billion to New York public schools, with more than half the money to be carved up between New York City and other urban districts. (A smaller portion would flow to SUNY and CUNY.)

When all’s said and done, a small amount of the state stimulus, perhaps as much as $1.5 billion over two years, would come without strings tightly attached. That’s only enough to undo a small portion of the $8 billion in tax hikes that Paterson has proposed for the same period.

The stimulus bills seem likely to breeze through the House, but Senate action will take a little longer. If Paterson really wants to avoid economically damaging tax hikes, he needs to join with other governors in insisting on greater flexibility in how states can use these funds.

It’s also a test for New York’s new junior senator. In the House, Rep. Kirsten Gillibrand lined up with fiscally moderate “Blue Dog” Democrats (although her voting record on a key index of tax-and-spending issues was indistinguishable from ultraliberal Rep. Barney Frank’s).

This is Sen. Gillibrand’s chance to stand up for a more financially responsible package and a better deal for New York taxpayers—even if it pits her against New York’s senior senator.