House Republicans are teeing up a vote this week on a new debt ceiling bill, marking the first legislative battle of President Obama's second term and one that could determine whether the country once again risks default over a political fight. 

House leaders, after unveiling the legislation Monday, are planning to hold a vote Wednesday on their plan to allow the government to keep borrowing through May 18. 

While the short-term increase is getting mixed reviews, the second plank of the legislation -- meant to pressure Senate Democrats to pass a budget -- has also raised questions.