Powerline has the best round-up of what House Republicans achieved:
So, what did the Republicans achieve? They put strings on the availability of funds beyond $250 billion, requiring fresh Congressional action for the last $350 billion. They added a requirement that Treasury establish an insurance program which would be funded by participating companies. This may be a big deal; I'm not sure exactly how it is intended to operate or how much, in the end, it will reduce the exposure to the taxpayer. They established a bipartisan oversight committee, rather than a committee run only by the Democrats, as Dodd and Frank had proposed. They took out special interest boondoggles for unions and for ACORN, the voter fraud organization. They removed a provision that would have allowed bankruptcy judges to arbitrarily reduce mortgages, an ill-conceived measure that would have aggravated a central cause of the current crisis, the difficulty of evaluating mortgage-backed securities. And they mandated a GAO study on the impact of the mark-to-market accounting rule, implicitly encouraging regulatory agencies to revise or abandon that principle, which is a key reason why banks that have little to do with the origins of the crisis are currently threatened.
The insurance approach was always central to the House Republicans' alternative to the Paulson and Frank-Dodd proposals. Whether their impact on the final product is profound, as opposed to merely helpful, depends on whether the insurance program is implemented and becomes a significant brake on taxpayer exposure.
The role played by John McCain appears to have been a constructive one. He supported and worked with the House Republicans. The Democrats no doubt wanted his support for the final product, and that must have enhanced the Republicans' position at the table. The Democrats would not have wanted an unpopular bailout plan to be supported by Barack Obama and opposed by McCain.