Ukraine crisis: An armed man in military fatigues on Wednesday stands guard outside a regional administration building seized by the separatists in the eastern Ukrainian city of Slavyansk.

FORTUNE — As the crisis in Ukraine intensified on Thursday with the reported deaths of up to five pro-Russian militants, it’s obvious the Obama administration’s economic strategy for supporting Ukraine isn’t working.

Mild economic sanctions, coupled with the threat of more to come, are imposing an economic price on Russia, but it’s not enough to change Russian policy and prevent the continued destabilization of Ukraine. Meanwhile, Western economic assistance conditioned on IMF-backed reform provides Ukraine with essential fiscal support, but is unable to halt the rapid decline of the Ukrainian economy, and the austerity demanded threatens a backlash in the east ahead of elections. The next round of sanctions, which could come in the next few days, presents the opportunity for a reassessment. It’s time for a change of course.

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The cost of the conflict on the Russian economy continues to mount. Russian asset prices have fallen, the currency has dropped despite a sharp rise in interest rates, and near-record high capital outflows are causing a tightening of financial conditions and a 5% fall in investment so far this year. Growth was negative during the first three months of the year, and is expected to be negative again in the second quarter. Overall, growth looks set to fall about 1½% this year. Downside scenarios where growth falls 4% or more are being circulated and discussed. Growth was weak even before the crisis, reflecting years of policy neglect and unaddressed structural weaknesses.

These dislocations come not from the sanctions that are already in place — such as visa bans and asset freezes on a limited number of Russians and a small bank associated with the Kremlin — but rather from the uncertainty about what comes next. Ambiguity works in favor of the administration here. Uncertainty about whether sanctions will be extended, and how they will be applied, creates a risk that is already having a chilling effect on financial relations. Anecdotally, banks are cutting back on their banking relationships and credit lines to Russian firms, selling assets and refusing to roll over maturing loans.

It is hard to ask more from the sanctions that have been put in place, and it’s reasonable to expect that their impact will grow over time. Yet, in policy circles, discontent is growing with the current strategy, as Russia seems undeterred by sanctions, and last week’s effort to create a truce of sorts seems to be failing. It also reflects the sense that Russian pressure is further weakening a Ukrainian government already under immense stress. Sanctions take time to work, and that in turn, requires stability in Ukraine.

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It is generally assumed that, should Russia explicitly invade Ukraine, Europe would side with the United States in implementing “sectoral sanctions” against Russian companies and banks. At the same time, in the current environment of Russian covert action in eastern Ukraine, Europe seems divided on extending the sanctions beyond lists of individuals. But if the U.S. is to act now, it needs a strategy that can succeed even without full backing from Europe. It also needs a Ukrainian government that can maintain popular support and make a successful transition after elections to a new, elected government.

Ukraine needs to be stabilized, and the government must be able to provide basic public services, and that requires money. The International Monetary Fund at end month is set to approve a loan package for Ukraine for a reported $17 billion over two years. But the headline number is deceiving. A sharp decline in activity, which the IMF estimates at minus 5% this year, an apparent collapse in fiscal revenue, and continued destabilization from Russia, mean that the program agreed now is likely to be off track in months if not weeks. The real purpose of the package is more short term in the sense that it would put in place some reforms and get Western money flowing to Kiev. In that regard, the program will be a success when the IMF’s board approves it. The day after approval, attention will shift to the program’s flaws, and uncertainty about future performance and disbursements could roil markets (as we saw, for example, in 2010 through 2011 in Europe’s peripheral countries as the region dealt with a debt crisis).

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Much of the debate over the package revolves around whether the austerity demanded by the IMF is appropriate for the moment. Consider the following imagined conversation between two Western policymakers:

Person one: “Ukraine’s economic problems are a legacy of weak policies under successive IMF programs. The measures demanded by the Fund are the minimum required — raising cost recovery of the energy company from 20% to 30% as the initial step of a gradual move to market prices, a well-targeted safety net for the poorest of consumers, and substantial financing for the government to smooth the necessary adjustments. Without reform, unsustainable economic policies will mean that Ukraine lurches from crisis to crisis.”

Person two: “A 50% increase in gas prices for households and a 40% hike for businesses will dramatically raise prices and lower household income, damaging confidence and demand at a time when the economy is already falling. Tax hikes and cuts to benefits, while needed in the long term, will further undermine support for the interim government. This plays into Russia’s hands.”

The problem is that both statements are true. Sadly, the risk is that the package is both too much and too little. It may be too much to be sustainable politically, and too little to make a material step toward sustainability. Ukraine’s track record of economic reform, even after the Orange Revolution, does not give much confidence that reform can be sustained even in favorable political circumstances.

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If the geopolitical case for supporting Ukraine is compelling, the West needs to provide better carrots and sticks. First, the U.S. should move forward with sectoral sanctions focused on cutting Russian banks and corporations from global financial markets. Because of Russia’s ties to global financial markets — integrated, highly leveraged, and opaque — financial sanctions can cause a sharp, rapid deleveraging that would result in significant economic distress for Russia. This is what I have called elsewhere, “Putin’s Lehman moment.”

U.S. financial sanctions can be effective even without Europe in full lockstep given the dominant position of U.S. banks and participation in the payments systems. Virtually all complex transactions will involve a U.S. financial counterparty at some point in the chain of transactions, and blocking one link in the chain can kill the transaction. It would be sufficient for Europe to support the sanctions informally (for example through tighter anti-money-laundering and tax oversight that would make sense in any context) and commit not to actively “fill in” as U.S. financial institutions step back.

At the same time, the West should make more of its financial support for Ukriane unconditional and not dependent of the IMF program remaining on track. This would insure that the government would not become hostage to further slippages and signal to Russia that the government has the durability to weather today’s shock. Together, these measures have a much better chance of avoiding an irreversible worsening of the crisis.

Robert Kahn is the Steven A. Tananbaum senior fellow for international economics at the Council on Foreign Relations in Washington, D.C. Previously, he was a senior strategist with Moore Capital Management. He also has held positions at the World Bank, IMF, U.S. Treasury, and Federal Reserve.