(CBS) -- Republican and Democratic leadership seem to agree on only one thing these days: An immigration reform bill that may or may not be comprehensive, may or may not further beef up border security and may or may not open a pathway to citizenship for 11 million undocumented immigrants currently living in the United States must make it to President Obama's desk - and soon.
With the threat of 2014 and 2016 politics creeping onto the horizon and August recess just weeks away, lawmakers from both parties and chambers hit the Sunday show circuit this weekend to stress the importance of overhauling the currently "broken" U.S. immigration system. But with the comprehensive package that soared through the Senate with meaty bipartisan support effectively dead on arrival in the GOP-controlled House, are both parties living in a pipe dream?
"They will act; they have to," Senate Majority Leader Harry Reid, D-Nev., said of the lower chamber during an appearance on NBC's "Meet the Press." "This is something that the vast, vast majority of Republicans, Democrats and independents support, and John Boehner should let the House vote. That's all he has to do. If the House voted, it would pass overwhelmingly."
House Speaker Boehner, R-Ohio, has been anything but coy about his opposition to bringing up the Senate's bill in the House, insisting on securing support from the "majority of the majority" of his caucus before introducing immigration legislation on the floor. On CNN's "State of the Union," Rep. Raul Grijalva, D-Ariz., called Boehner's approach "anything but encouraging," and conceded immigration reform prospects are "not looking good."
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It's a matter of methodology - Republicans are insisting on tackling their version of the bill piecemeal, via regular order - as well as substance; namely, border control. The Senate, before passing its version of the bill last month, tacked on a robust and pricey border security amendment to attract maximum GOP backing - a move some more conservative House Republicans have cited as "candy" to get votes.
Appearing on "Face the Nation," Sen. Dick Durbin, D-Ill. - a member of the "gang of eight" senators who crafted the chamber's immigration legislation - argued that as demonstrated by the Senate, reform "can't be done by the Republican conference in the House; it should be done on a bipartisan basis." The No. 2 Senate Democrat worried that some opponents of the bill may never be happy with the amount of border control.
"We started this debate, started this conversation among Democrats and Republicans, with two basic understandings - first, a path at the citizenship," Durbin said. "Folks have to come forward and register, pay their taxes, pay a fine, be monitored to make sure they have no criminal background that troubles us. Give them a chance for 10 years to pay taxes and not receive government benefits and then an opportunity of the three-year path to legalization. ...It's certainly not amnesty.
"And we said to the Republicans, 'All right, I will give when it comes to the border,'" he continued. "Do I think we're overspending in our bill on border security? Yes, I do. But on the Republican side they insisted on it, we agreed to it and came up with 14 Republicans who said this is a fair way to reduce the likelihood of illegal immigration. ...I'm afraid when it comes to this border security, there's never enough for some. They say it's about border security that's a reason they can't be for immigration reform. I think it's about something else."
Rep. Steve King, R-Iowa, one of the most outspoken opponents of immigration reform, seemed to corroborate that theory on "Fox News Sunday," arguing that all the border control amendments in the world wouldn't ensure the administration will enforce the measure. "We cannot fix with laws things the president refuses to do," he said.
Stipulating that no one is "satisfied with the status quo on immigration" and that he hopes "the House will be able to move forward on something" that could enter conference, Senate Minority Leader Mitch McConnell, R-Ky. - who voted against the Senate bill - predicted on NBC that the "key to getting a final outcome" is to "seriously beef up" border control. "The question is can we actually get the border secure and not have this happen again - that's the stickiest issue," he said.
On "Face the Nation," Rep. Mike Kelly, R-Pa., agreed that when he asks his constituents what the most important thing is to them about immigration, "They say, 'Oh, my goodness - our borders are too open. We have too many people coming in.
"They say, 'Listen, we were promised before the 1986 [reform] that we would have border security; everything would be taken care of,'" he continued. "At that time I think it was a three and a half million undocumented immigrants here. Now they say 11 and a half to 12 million. And we say, you know what you look back in history and the old saying is, 'those who do not study history are doomed to repeat it.'"
But despite resistance from Reid and other top Democrats, as well as border security skeptics on the right, some lawmakers from both sides made the case Sunday that the House's regular-order approach could be just the ticket for reconciling disagreements. Rep. Chaka Fattah, D-Pa., on CNN opined that by going to conference to merge the House and Senate bills, "we will pass" some type of reform legislation. "I'll be asking my House colleagues when we come up for any type of vote on this to offer the Senate bill as the Democratic alternative.
"Let's get to a vote," he said.
Summarizing conclusions from an hours-long meeting last week with the entire House GOP Conference, Kelly admitted deporting 11 million illegal immigrants "doesn't make sense."
"Is there a path to citizenship? I think there is." But, he added, the House approach "is about breaking it into separate pieces, having a really thoughtful and a healthy debate about it and then doing something that makes sense for the American people. If we can't do that, then shame on us."
Rep. Mario Diaz-Balart, R-Fla., during the same segment, defended that view: "In the House, we are going to do it right. We're going to do it methodically. I think, ultimately, we're going to get a better piece of legislation. ...We're not going to have to pass it to find out what's in it. We're going to take our time, get good legislation."
Kelly granted that the debate about immigration reform has "been going on for years," but qualified it "hasn't reached the peak it's at right now." Diaz-Balart added that "what's changed now is that there's a realization... that we have to fix this broken immigration system that is affecting us. It's affecting our economy, our national security, et cetera.
"So unlike when the Democrats controlled and unlike in previous years when the Republicans controlled," he continued, "I think there's the realization, particularly, by the Republican leadership that we have to get it done but, more importantly, we have to get it done right to protect the economy, to protect the rule of law, dealing with the folks that are here while not violating the rights of the folks who have done things legally. And obviously, in a way that's thoughtful, responsible, and very clearly enforceable."