Senate Banking Chairman Chris Dodd (D-Conn.) and House Financial Services Chairman Barney Frank (D-Mass.) emerged from the White House on Friday predicting they would send a financial reform bill to President Barack Obama before July Fourth.

The two met with Obama to map out the next steps for the financial reform bill, which cleared the Senate Thursday night on a 59-39 vote. Frank reiterated his call to televise the conference committee process while Dodd pledged to smooth out differences between the House and Senate versions of the legislation.

“We will have a conference, I think, that will work well,” Frank told reporters after the White House meeting. “It will be conducted, the formal parts, in public. That means that no agreements reached, no compromises, which obviously are being discussed, will be made part of anything without being publicly presented and voted on and discussed.”

Key issues that will have to be ironed out between the chambers include how best to organize a consumer protection agency, whether to regulate auto dealers under the new financial regulations and how stringent new rules on the derivatives market should be. Those issues were the subjects of intense floor debate in the Senate, and Dodd is expected to try to persuade House negotiators to keep the final bill close to the one he authored in his chamber.