The Federal Reserve is set to vote on Wednesday on Capital One’s $9 billion acquisition of ING‘s online banking unit in the United States.

The proposed takeover, announced in June, is among the first bank mergers to face regulatory scrutiny for its impact on the broader economy. Under the Dodd-Frank law, the financial regulatory overhaul passed in response to the financial crisis, the Fed must now weigh systemic risk when evaluating a deal – and shut down an acquisition that is likely to endanger the economy.

Critics say Capital One’s acquisition of the unit, ING Direct USA, will do just that. The takeover would transform Capital One into the nation’s fifth-largest bank by deposits, leaping from the No. 8 spot. The deal drew criticism during a rare round of public hearings last year, when consumer advocates and community bankers argued that the merger would create another “too big to fail” bank.

Despite the controversy, the firm has sounded an optimistic tone about winning approval for the deal. In an earnings announcement last month, the bank’s top executives said they hoped the Fed would rule during the first quarter of 2011. Initially, the bank envisioned closing the deal between late last year and early 2012.

“We remain on track,” Richard D. Fairbank, Capital One’s chairman and chief executive, said on a recent conference call with analysts, adding that deal would be “game changing” for the bank.

For now, the deal’s fate rests with the Federal Reserve Board governors, who will meet in Washington on Wednesday afternoon.

Capital One needs support from a majority of the board’s five governors to secure approval. It is also possible the Fed will approve the deal on the condition that Capital One sheds certain assets or increases lending in low-income areas, moves that might appease critics.

The deal is part of Capital One’s broader effort to expand its footprint across the country. The bank announced plans last year to buy HSBC’s American credit card business for $2.6 billion, a deal that the bank hopes will gain regulatory approval later this year.

With ING, Capital One agreed to pay $6.2 billion in cash for the firm’s online banking unit in the United States. Under the terms of the deal, Capital One would also issue $2.8 billion worth of new shares to ING, giving the Dutch firm a 9.9 percent stake.

Consumer advocates objected immediately. Led by the National Community Reinvestment Coalition, the advocacy groups cast the deal as a risk to taxpayers and painted the firm as a risky subprime lender. About a third of Capital One’s credit card portfolio carries the subprime label, defined as loans to borrowers with credit scores below 660, according to the company.

The Fed, responding to pressure from consumer groups and Democratic lawmakers, held three public hearings on the deal.

While the contentious hearings provided a forum for critics to assail the deal, the bank also took the chance to defend its reputation. The deal, Capital One’s general counsel said, would actually reduce systemic risk because the combined banks were run-of-the-mill lenders that shun risky Wall Street businesses.

Whether the Fed agrees is a matter of great importance for the banking industry. The Fed’s decision could have a broader impact on deal-making among banks, especially if the governors spells out for the first time what constitutes a systemically risky acquisition.

The Fed also might acknowledge that the deal poses some risks to the economy — but approve it nonetheless.

“While Congress instructed us to consider the extent to which a proposed acquisition would pose a greater risk to financial stability, it clearly did not instruct us to reject an acquisition simply because there would be any increase in such risks,” Daniel K. Tarullo, a Federal Reserve Board governor, said in a speech last year.