According to a new Gallup poll Wednesday, the Republican party's favorable rating dropped to 28%, down 10 percentage points from September. The 43% for Democrats was a 4-percentage-point drop from last month.
Senate Democrats sought to keep up the pressure, holding a rally on the Capitol steps on Wednesday to demonstrate their unified stance in calling for House Republicans to reopen the government and raise the debt ceiling.
A CNN survey indicates enough Republicans in the House would join Democrats in voting for a Senate-passed spending plan to end the shutdown.
All 200 Democrats and 19 Republicans support passing a continuing resolution with no additional legislative strings attached .
With two vacancies in 435-member House, 217 votes are currently the minimum needed for the measure to win approval in the House.
However, not enough Republicans are willing to join Democrats in a procedural move to force Boehner to hold a vote on the Senate plan.
Boehner has said the measure would fail to pass in the House, a contention rejected by Obama and Democrats.
The speaker has previously allowed measures to pass the House with mostly Democratic support, which has weakened his leadership among conservatives. Doing so now could cost him his leadership post due to the conservative backlash in would likely unleash, analysts believe.