Approval of the rule followed a highly predictable floor debate in which Republicans said the government can't afford the pay hike, which will cost $11 billion over the next decade. Democrats countered that the bill is an attempt by Republicans to continue picking on federal workers who have had their pay frozen for the last two years.

"The Republicans have decided that they want to continue in the same short-sighted and counterproductive campaign against federal employees that we saw in the last Congress," Rep. Alcee Hastings (D-Fla.) said.

Rep. Rob WoodallWilliam (Rob) Robert WoodallHouse GOP pushes hard-line immigration plan as Senate deals fail Womack wins initial support to become Budget chairman This week: Clock ticks toward shutdown deadline MORE (R-Ga.), who managed the rule on the floor for Republicans, said the issue is the need to control the deficit, not the performance of federal workers.

"You will not find one finding of contempt for federal employees," he said. "In fact, if you listened to the hearing in the Rules Committee last night, what you saw was universal praise for the hard work that our men and women in the civil service are doing for this country."

Woodall also criticized Democrats for claiming to want to support middle-class families that work for the federal government after they have supported the policies of President Obama, which added tens of thousands in public debt that these same families will ultimately have to pay off.

Democrats complained throughout the debate that the bill should be split in two, because it would freeze the pay of both federal workers and members of Congress. Rep. Jared Polis (D-Colo.) accused Republicans of combining the two because of the difficulty some might have voting against a bill that limits congressional pay.

"This rule and this bill suffer from the stench of politicization, and the House should divide these two issues," Polis said.

As they have all week, Democrats also complained that Republicans should be working on a bill to avoid the sequester. But that debate fell on deaf ears, as Republicans have said they will not take up any bill unless and until the Senate passes one.

Before the vote on the rule, members debated whether to take up the rule at all, after Polis raised a point of order against doing so. But Polis acknowledged that his point of order was mostly meant as a way to object to the way the bill is bring brought to the floor: without committee consideration.

Members agreed by voice vote to take up the resolution, and Democrats did not call for a roll-call vote.

In addition to the pay freeze bill, the rule also allows the House to consider a resolution on Friday that condemns North Korea's recent nuclear testing.