In the coming days, the House GOP campaign arm will launch a polling project to gauge whether to invest in three other blue congressional districts that have only recently come onto the national radar, according to two sources familiar with the deliberations. Two of them comprise the eastern, more liberal half of Iowa. The other is in Obama’s native Hawaii.

The goal is to broaden a political map that, much to the GOP’s frustration, has remained stubbornly narrow. Thanks to a recent round of redistricting that limited the number of seats vulnerable to an opposing party takeover, the House playing field comprises only around three dozen districts. If the election were held today, Republicans, who currently have a 17-seat majority, would gain perhaps six or seven seats — short of the 11-seat benchmark they’ve set.

So the GOP is venturing into places one wouldn’t expect. The stakes are high: Republicans are trying to achieve a governing majority, something that has eluded John Boehner in his tenure as speaker. If they can meet their 11-district goal, Republicans will have 245 seats, their largest delegation since 1949. It would also give the party a buffer heading into a 2016 House election expected to be more generous to Democrats.