SUGAR LAND, Texas — President Bush said terrorists will win if Democrats win and impose their policies on Iraq, as he and Vice President Cheney escalated their rhetoric yesterday in an effort to turn out Republican voters in next week’s midterm elections.

Democratic operatives continued to broaden the field of races they believe are competitive enough to merit last-minute investments, as the party’s House election committee launched ads in typically conservative districts of Kentucky, Nebraska, and Nevada. In the Senate battle, new public and private polls yesterday indicated very tight races in Tennessee, Virginia, and Missouri, the last of which is shaping up as possibly the country’s tightest contest.

Faced with potential GOP defeat in both chambers, Messrs. Bush and Cheney aimed to avert that by convincing voters that they cannot risk giving the opposition party any power in Washington.