Capping off a month of intense negotiations on health care reform, a bipartisan group of Senators who serve on the Finance Committee released a statement Thursday pledging to continue their effort to reach a consensus on legislation when Congress returns from its July Fourth recess.

The statement, signed onto by Finance Chairman Max Baucus (D-Mont.) and ranking member Chuck Grassley (R-Iowa), comes after a week of furious negotiations on a bipartisan health care bill. Lending their names to the statement were Senate Budget Chairman Kent Conrad (D-N.D.); Health, Education, Labor and Pensions ranking member Mike Enzi (R-Wyo.); and Sens. Jeff Bingaman (D-N.M.), Orrin Hatch (R-Utah) and Olympia Snowe (R-Maine).

“Reforming America’s health care system is a tremendous challenge, but it’s a challenge we simply have to face,— the Senators said. “The issues facing reform are difficult and complex, but over the past several months, we’ve made progress toward workable solutions. As we have been for the last several weeks, we are committed to continuing our work toward a bipartisan bill that will lower costs and ensure quality, affordable care for every American.—

Various members of the Finance Committee met privately at least three times on Thursday but were not scheduled to meet again until after the July Fourth break. Although Baucus indicated that committee members were getting closer to a bipartisan agreement, he declined to speculate about when he would be able to begin marking up a bill.

Baucus’ enthusiasm is due in part to a recent Congressional Budget Office score of various policy options that puts the costs of a bill at less than $1 trillion over 10 years. The CBO also has scored those options as deficit neutral. Baucus revealed this information to reporters earlier Thursday.

“It’s now a process of, where does the support lie— for various policies, Conrad said.

The HELP Committee, which began marking up its bill last week, concluded its markup work Thursday afternoon and was not scheduled to reconvene until after the recess. Once Finance and HELP have finished their markups, they will merge their bills into one measure.

President Barack Obama has demanded that Congress send him a health care reform bill no later than Oct. 15. The House and Senate hope to clear bills out of their respective chambers before Congress adjourns for the August recess.