House Republican leaders signaled for the first time Thursday that they intend to get back to business, in a matter of days, after the tragic shooting in Tucson temporarily derailed plans to kick off the 112th Congress with a series of votes aimed at cutting spending and growing jobs. 

At the top of Republicans' agenda was a contentious vote on repealing the health care law. They called off that vote in the House, originally scheduled for Wednesday, after Rep. Gabrielle Giffords and 19 other people were shot over the weekend by a lone gunman. 

But a spokesman for House Republican Leader Eric Cantor told Fox News on Thursday that Congress will push ahead with "thoughtful consideration" of the bill next week. Several other House Republicans echoed the need for Congress to resume its agenda, having paused out of deference to Giffords and the families of the victims for a full week. 

"We don't need to be wasting time," Rep. Phil Gingrey, R-Ga., told Fox News. "We can walk and chew gum at the same time." 

In light of President Obama's well-received speech Wednesday in which he called for a more civil discourse in American politics, the timetable poses a risk for the new House majority. Moving too forcefully opens the door for Democrats to accuse the party of ignoring the president's advice. 

A House Democratic aide suggested they will be monitoring the tone carefully in Washington. 

"There is widespread recognition that both sides need to choose their words more carefully when discussing these issues and reflect on the impact those words have," the aide told FoxNews.com. "The health care debate will be the first real test of whether or not this will be the case." 

That debate is for many lawmakers the marquee example of where the public discourse became most vitriolic over the past two years. Obama said during the memorial service in Arizona on Wednesday that lawmakers owe it to the victims to tone it down. 

But he also quieted suggestions that the political grandstanding and high-octane commentary of the past two years somehow drove alleged shooter Jared Loughner to the point of violence. 

"It did not," Obama said. 

No doubt mindful of the potential pitfalls, Republicans pledged Thursday to proceed respectfully in the days ahead. 

"Americans have legitimate concerns about the cost of the new health care law and its effect on the ability to grow jobs in our country," Cantor spokesman Brad Dayspring said. "It is our expectation that the debate will continue to focus on those substantive policy differences surrounding the new law." 

House Republican Whip Kevin McCarthy, R-Calif., said Thursday that the tenor of debate going forward will be focused primarily on jobs creation. He said lawmakers will get back to work while keeping Giffords in their thoughts and prayers. 

Obama announced Wednesday night that Giffords had for the first time opened her eyes in response to those around her, a development McCarthy cited as great progress. 

The call for legislative business to resume does not mean things are necessarily back to normal. Lawmakers now are far more attuned to legislation dealing with personal security. Rep. Louie Gohmert, R-Texas, plans to introduce a bill authorizing members of Congress to carry guns in the District of Columbia and in the U.S. Capitol. 

House Speaker John Boehner also announced that Arizona Republican Rep. Jeff Flake will deliver the party's weekly radio address on Saturday. Flake is one of the leading crusaders on Capitol Hill against earmarks and wasteful spending. But the address was pitched solely as a dedication to the victims of Saturday's shooting and the citizens who intervened. 

"I'm proud on behalf of House Republicans to deliver this address honoring the victims of the shooting in Tucson, Arizona, and thanking the heroes who acted selflessly in the face of violence," Flake said in a written statement. 

FoxNews.com's Judson Berger and Fox News' Chad Pergram contributed to this report.