House Republican leaders on Sunday showed no signs that their party would accept the Senate's bill to overhaul the nation's immigration laws, instead suggesting that they want to address the issues one by one.

"We are not going to take up the Senate bill in the House, because we don't support the Senate bill," Rep. Paul Ryan (R-Wis.) said on CBS's "Face the Nation". "What we're going to do is take a step-by-step approach to get immigration right -- not a big, massive bill, but separate bills so people know what's in these bills."

House Majority Leader Eric Cantor (R-Va.) echoed those sentiments during an interview on Fox News Sunday, indicating that the House would take a piecemeal approach to dealing with immigration.

"We will have a vote on a series of bills at some point," Cantor said. "And it will deal with a variety of issues. Border security is a really important issue because it goes to that trust factor."

Ryan also insisted that border-enforcement legislation should come first. He added that his party opposes amnesty for undocumented immigrants and wants to instead give such individuals a chance to "get right with the law."

"That means go on probation," Ryan said. "You have to do certain terms of probation, and it's a one-strike policy if you don't meet the conditions of your probation."

Asked whether the Republican stance on immigration could pose a political risk, Ryan responded: "We want to get it right and do what's right for national security and economic security. And our motivation is not what's good for us politically, because if we just think like that, we're not going to do this the right way."