Under Dodd-Frank, banks cannot make certain swaps trades, such as those that relate to commodities, equities and credit. The aim of this restriction was to reduce the risk exposure of these banks, since derivatives trades were seen as a factor in the 2008 financial collapse.

But supporters of the bill argue that many financial institutions need these swaps trades to hedge risk, and that not all of these swaps trades carry dangerous levels of risk.

The bill, from Rep. Randy Hultgren (R-Ill.), would repeal most of Section 716 of Dodd-Frank, which puts in place swaps restrictions on banks. However, the bill keeps in place language in that section that prohibits the use of taxpayer funds to bail out swaps entities.

The House Financial Services Committee approved the bipartisan bill back in May, when Chairman Jeb Hensarling (R-Texas) said current law is making it harder for companies to hedge risk, and therefore making it harder for them to hire.

"At a time when far too many of our fellow countrymen remain unemployed or underemployed, the derivatives title is a critical one for those who are seeking employment to find work," he said. "We have heard from our framers, our ranchers, our factory owners, from end users, how problematic the current interpretation of these laws may be."

The bill is co-sponsored by Reps. Jim Himes (D-Conn.), Richard Hudson (R-N.C.) and Sean Maloney (D-N.Y.).

The second bill up next week is H.R. 2374, the Retail Investor Protection Act. This bill, from Reps. Ann Wagner (R-Mo.) and Patrick Murphy (D-Fla.), would put limits on the ability of the Department of Labor to issue rules expanding fiduciary responsibilities to a wider range of financial professionals that serve retail investors.

Dodd-Frank gave the Securities and Exchange Commission (SEC) the authority to issue rules on which financial advisers should be considered fiduciaries. But the Department of Labor has indicated it wants to issue rules in this area, and the bill from Wagner and Murphy would require Labor to wait until 60 days after the SEC acts.

The bill's sponsors argue that new rules would likely increase the costs of seeking financial advice, and thus make it harder for retail investors to obtain this advice.

The bill would also require the SEC to examine whether new rules on fiduciary responsibilities would limit access to financial products, before it acts. Dodd-Frank allows the SEC to issue a rule in this area, but does not require a rule.