WASHINGTON  A costly and polarizing Congressional campaign heads into its closing week with Republicans in a strong position to win the House but with Democrats maintaining a narrow edge in the battle for the Senate, according to a race-by-race review and lawmakers and strategists on both sides.

President Obama campaigned for a fourth consecutive day on Saturday as the Democratic Party threw its full weight into preventing a defeat of historic proportions in an election shaped by a sour economy, intense debate over the White House’s far-reaching domestic agenda and the rise of a highly energized grass-roots conservative movement.

But Republicans have placed enough seats into play that Democrats now seem likely to give up many of the gains they made in the last two election cycles, leaving Washington on the brink of a substantial shift in the balance of power.

The final nine days of the midterm election are unfolding across a wide landscape, with several dozen House races close enough to break either way, determining whether the election produces a Republican wave that reaches deep into the Democratic ranks. In the Senate, Democrats were bracing to lose seats, but the crucial contests remained highly fluid as Republicans struggled to pull away in several Democratic-leaning states.