The other bills face strong opposition. In fact, one member of the committee, Rep. Ed Royce, R-Calif., said he envisions the "new normal for insurance regulation" being "a hybrid model with layered regulation by states and the federal government."

Royce concluded that "regulation can take place at the federal level, but it must be smart and specific to insurance-operating models."

Two bills, H.R. 605, The Insurance Consumer Protection and Solvency Act of 2013, and H.R. 4557, the Policyholder Protection Act of 2014, would limit the ability of the Federal Deposit Insurance Corporation to assess insurance companies to pay for failing banks or thrifts, whether they are non-bank SIFIs or troubled institutions that are owned or controlled by insurance companies.

In general, these two bills would require states to agree for an insurance company to be assessed for the insolvency of any troubled financial services company.

Another bill, the Insurance Data Protection Act, proposed by Rep. Steve Stivers, R-Ohio, would limit the authority of the Federal Insurance Office (FIO) and the Office of Financial Research (OFR) to subpoena data from insurance companies, requiring that the FIO:

• Obtain approval from the Secretary of the Treasury.
• Verify that such data is not available through the insurance company's state regulator, another federal agency, or a public source.
• Agree to reimburse insurance companies for the cost of producing the data. The bill would also require federal entities and state regulators to maintain the confidentiality of nonpublic data obtained from or shared with other federal and state regulators.

The Independent Insurance Agents and Brokers of America voiced strong support for the Insurance Data Protection Act, as well as H.R. 4510 and H.R. 4557. As for the Data Protection Act, the IIABA said the FIO and the OFR "possess sweeping subpoena power that can be abused if suitable safeguards are not put into place, and this proposal would institute appropriate procedural protections that must be satisfied before these entities may demand the production of information in this manner."

In commenting on the legislation, Thomas Karol, federal affairs counsel for NAMIC, says although every publicly traded company, including insurers, must file GAAP statements with the Securities and Exchange Commission, many mutual insurance companies prepare financial statements using SAP only.

"Forcing such companies to prepare GAAP statements in addition to SAP is a labor intensive, multi-year project that will cost companies hundreds of millions of dollars without adding any benefit in regulating the company," Karol says.

As for the Insurance Data Protection Act, Karol says, "Data calls and document productions are costly and time-consuming endeavors for insurers and raise issues related to the confidentiality and security of the information," Karol said. He adds, "NAMIC recognizes the need for information at the federal level, but believes that collection of information should be limited."

Joseph Kohmann, chief financial officer and treasurer of the Westfield Group, testified on behalf of PCI, stating, "PCI and Westfield support strong regulation," but "our growth is being restrained by unintended consequences stemming from an expansion of banking regulation in the Dodd-Frank Act that conflicts with state-insurance regulation."

As to H.R. 605, the Insurance Consumer Protection and Solvency Act, Kohmann said that this legislation ensures that resolution of insurance companies and their assets is conducted by insurance regulators, not by a federal banking agency. "It would also prevent the FDIC, primarily responsible for bank resolutions, from using insurance assets to support failing banks." Kohmann says.

He adds, "Insurers are already responsible for resolving their own failures and pay for guaranty funds in every state to protect consumers. Don't let insurance policyholder protection funds be used to support risky investment firms and banks."

The American Insurance Association (AIA) said in a statement, "Our members have a strong interest in ensuring that implementation of the Dodd-Frank Act carries out Congressional intent and aligns with the insurance business model and the regulatory system that flows from that model."

The association said it supports the proposal enabling the Federal Reserve to create capital rules specifically tailored to the insurance industry. Further, AIA said it welcomes H.R. 4557.

"AIA looks forward to working with Congress, our industry's regulators, and other stakeholders to ensure that insurance regulatory modernization and implementation of the Dodd-Frank Act, as applied to property and casualty insurers, reflects the insurance business model and promotes market competition while protecting policyholders."

Daniel Schwarcz, an associate professor at the University of Minnesota Law School and a consumer advocate for the National Association of Insurance Commissioners, voiced concern over some of the proposals.

He said that some of the proposed bills "unwisely interfere" with the federal government's ability to appropriately regulate and monitor the insurance industry.

"A common theme in the provisions that I identify is that they unduly limit the ability of federal agencies to regulate, identify, or respond to new and emerging sources of systemic risk in insurance markets," Schwarcz said.

"Given the importance of insurers to the 2008 financial crisis and the potential for insurers to pose various new types of systemic risks in the future, imposing excessive restrictions on federal agencies charged with regulating or monitoring systemic risk in insurance is unwise," he added.

And, in a note issued in late 2011, Moody's Investors Service said if a bill rolling back the Federal Insurance Office's authority should pass, it would limit financial transparency and the effectiveness of regulatory supervision.

Additional reporting by Tim Sprinkle.