Speaker John A. Boehner (R-Ohio) sought to temper expectations last week by suggesting that it will be incredibly difficult for the House to make any progress on immigration reform this year.

While prospects for immigration bills remain slim in the House this year, Boehner didn't rule out the possibility that at least some proposals might earn a vote in the coming months. And on Sunday, one of Boehner's closest allies, Rep. Tom Cole (R-Okla.), noted that several lawmakers are still working on the issue.

"I think step-by-step progress is still out there," Cole said on ABC's "This Week." "Whether or not Democrats want to work that way I think it's unclear, but you could clearly get a border security bill through, I think you could get HB-1 [sic] visas through, I think you could get seasonal labor through. I think there's still a path there. But I think that's recognizing political reality -- there's a lot of division on the issue."

Capitol Hill reporters know that Cole is always a reliable gauge of what top GOP leaders are thinking and doing -- so his brief comments signaled that leaders haven't entirely given up. If Cole is correct, then which proposals might still have a chance of earning some floor time? Let's recap what's out there:

Potentially in the mix:

(Nick Miroff/Post)

House Homeland Security Committee border security bill: When Cole talks about getting "a border security bill through" the House, this is one of the options he's talking about. The Homeland Security panel unanimously approved its proposal last spring. Read that again: Every Republican and Democrat on a committee in the bitterly divided 113th Congress voted to approve a bill. If Republican leaders are looking for a way to start the immigration debate in a bipartisan way, this bill would be a safe bet.

The measure instructs the Department of Homeland Security to come up with plan to secure the U.S.-Mexico border that ensures the apprehension of 90 percent of illegal border-crossers in high-traffic areas within 33 months and across the entire border within five years. It also instructs DHS to find ways to deploy along the border military-issued radar, cameras and unmanned aerial drones coming recently used in Iraq and Afghanistan. Many close observers fear the plan doesn't do enough to allay the concerns of lawmakers worried about border security -- but it would be hard for GOP leaders to ignore this bipartisan proposal.

(AP Photo/Matt York, File)

The House Judiciary Committee's four bills: The panel approved four proposals along party lines in late June that deal with the legal status of illegal immigrants, agricultural guest workers, green cards for highly-skilled workers and changes to the E-Verify program.

When Cole talks about debating bills regarding "HB-1 visas" and "seasonal labor," these are some of the leading options. (Cole misspoke when he called them HB-1 visas -- they're officially known as H1-B visas.)

H1-B visas are granted to highly-skilled, highly-educated immigrants -- and a bill called The SKILLS Act would set new rules on how many green cards could be granted each year to certain types of highly-skilled immigrants. The proposal Cole mentioned regarding agricultural guest workers is called The AG Act and would establish a new system for guest farm workers to enter and exit the U.S. for 18-month periods.

The two other bills passed by the committee were the SAFE Act, which would make it a crime for illegal immigrants to be in the United States, and the Legal Workforce Act, which deals with changes to the E-Verify program. Their fate is less certain -- but changes to E-Verify are seen as a must. E-Verify is an Internet-based system that allows businesses to determine whether or not workers are legal immigrants.

Supporters of the Maryland DREAM Act march from Silver Spring to Wheaton in August 2012. (Matt McClain/for The Washington Post)

The Kids Act: This it the working title of a bill that aides privately describe as the GOP alternative to the DREAM Act, a bipartisan plan that would allow the children of illegal immigrants to eventually obtain U.S. citizenship if they meet certain requirements and go to college or serve in the military.

House Majority Leader Eric I. Cantor (R-Va.) and House Judiciary Committee Chairman Bob Goodlatte (R-Va.) are taking the lead on this proposal and both have been incredibly tight-lipped about their work. Cantor wants to see the House move ahead with immigration, but hasn't pushed as boldly as Boehner. He suggested in a speech at the American Enterprise Institute last year that the House's work on immigration reform should begin by focusing on the children of illegal immigrants.

If Cantor and Goodlatte ever release a bill, it will be only after carefully gauging support among rank-and-file Republicans.

Dead in the House:

Five of the eight members of the Senate's immigration "Gang of Eight." (The Washington Post).

The Senate "Gang of Eight" bill: Senators approved this plan 68 to 32 in late June -- making it the only piece of immigration legislation to pass either chamber in the past two years. The $50 billion measure would double the number of U.S. Border Patrol agents along the southern border and require the construction of 700 miles of fencing there. It would set millions of eligible immigrants on a 13-year course toward achieving permanent residency status or U.S. citizenship after paying thousands of dollars in fines and back taxes. But none of that matters -- House Republican leaders have vowed never to introduce the measure.


House Minority Leader Nancy Pelosi (D-Calif.), Assistant Minority Leader James Clyburn (D-S.C.) and House Minority Whip Steny Hoyer (D-Md.). (Melina Mara/Post)

The House Democratic "replacement bill:" Democratic leaders quietly unveiled it last October during the government shutdown. The measure would amend the Senate immigration bill by striking its border security provisions and instead swap in the border control plan unanimously approved by the House Homeland Security Committee (see above). House Minority Leader Nancy Pelosi (D-Calif.) and her lieutenants introduced the measure and often cite freshman Rep. Joe Garcia (D-Fla.) as one of its leading proponents. But here again the effort is fruitless, as House GOP leaders are almost certain to never seriously consider it.

Rep. Luis Gutierrez (D-Ill.) an active member of the now-defunct House "Group of Eight." (Washington Post)

The bipartisan "Group of Eight" talks in the House: Not to be confused with the Senate's "Gang of Eight" (see above), this group tried and failed to agree on a bipartisan proposal. The group included Reps. John Carter (R-Texas), Sam Johnson (R-Texas), Raul Labrador (R-Idaho), Mario Diaz-Balart (R-Fla.), Luis Gutierrez (D-Ill.), Xavier Becerra (D-Calif.), Zoe Lofgren (D-Calif.) and John Yarmuth (D-Ky.).

But Diaz-Balart is still working on immigration proposals and admitted in an interview with The Washington Post last week that he's using some parts of the group's work to write new proposals on border security and the legalization of the nation's 11 million immigrants. He liked parts of the bill so much that he keeps a copy of it in a thick black binder on a his desk.

Thoughts? What did we miss? The comments section awaits your thoughts.