Not sure how to make it happen, perhaps different Obama rhetoric around guns and coal? Avoiding "clinging to guns and religion" might help there. Earlier and greater evidence linking his wife to cocaine and/or corruption could work.
Without McConnell in the caucus the total obstruction line might not become GOP strategy, but the Dem's majority would also be less vulnerable to fillibusters and Joe Liebermans. The filibuster would likely thus be a less contentious issue overall. We'd also likely see a better stimulus bill, a public option in Obamacare, and many more judicial confirmations. Conceivably some republicans would be more open to bipartisanship on stuff like climate and immigration in this scenario. Even if not, the marginal improvements in 2009-2010 would have a big impact on the 2010 midterms, even if they didn't swing them completely. They, and that 2010 electoral change, would also give Obama much broader support and potential in the later years, so you'd probably see some Bush tax cut repeals sooner, less austerity, and maybe even an actual treaty on climate or Iran going before the Senate.