Although many Senate Democrats say that liberal priorities such as climate-change legislation have fallen off Obama’s agenda, they also see an opportunity to begin a political recovery by pursuing more moderate legislative goals with Republicans’ help.

“We’re going to try to ease out onto the frozen lake,” a senior Democratic leadership aide said of the GOP outreach effort. “If it starts to crack, we’ll run back.”…

Another early test could come when the Senate attempts to change a provision in the health-care law that small-business owners say would overly burden them with new paperwork requirements. Democrats are eager to find out whether Republicans confine their broader repeal efforts to that one debate.

The new centrism also could come into focus during a trade debate expected to begin as soon as February. Congress must reauthorize a program that assists workers who lose their jobs as a result of a rise in imports, an opportunity for free-trade supporters to offer a pending trade agreement with South Korea. In his speech on Tuesday, Obama said the South Korea pact could create 70,000 American jobs and urged Congress “to pass it as soon as possible.”