WASHINGTON — A woman who appears in an advertisement supporting Representative Jon Runyan, a New Jersey Republican, boasts about how he works “with both parties.”

Richard E. Mourdock of Indiana, whose Senate campaign has been most notable for his derision of legislative compromise as feckless, now says he would “work with anyone.”

While out and about on the campaign trail, Representative Bobby Schilling, Republican of Illinois, talks so much about all the great things he has done with Representative Dave Loebsack, a Democrat from nearby Iowa, that one would think the two were related.

Partisan obstreperousness, the force that propelled Congressional Republicans to widespread victory in 2010, is suddenly for many of them as out of style as monocles. In campaign advertisements, some lawmakers who once dug in against Democrats now promote the wonders of bipartisanship. And legislatively, Republicans in tough races are seeking to soften their edges by moderating their votes, tossing their teacups and otherwise projecting a conciliatory image to voters.