Two top House Republicans rejected the idea of pursuing a series of piecemeal deficit-cutting agreements in exchange for gradual increases in the government's borrowing limit, putting more pressure on negotiators to start cutting deals on a broader package within days.

Vice President Joe Biden is leading a bipartisan group of lawmakers seeking to craft a plan for reducing the federal budget deficit, hoping it will ease the way for an increase in the government's $14.29 trillion debt ceiling.

Most...