We live in very strange times. The deep dysfunction that has gripped our political system for the past several years has not disappeared. If anything, it is even more pronounced in the House of Representatives and in many states. But at the same time, there are prospects, serious prospects, for major advances in a number of key policy areas that have stubbornly eluded commonsense solutions or breakthroughs. President Barack Obama has the usual challenges that face any second-term, lame-duck president, ones that make serious new policy advances unlikely — and with the additional hurdle of vicious, tribal politics — but there are serious possibilities that he could have a strikingly successful second term.

The latest sign of green shoots is, of course, the immigration reform plan laid out earlier this week by the “gang of eight,” an impressive group of senators including Democrats Charles E. Schumer of New York, Richard J. Durbin of Illinois, Michael Bennet of Colorado and Robert Menendez of New Jersey and Republicans John McCain of Arizona, Lindsey Graham of South Carolina, Jeff Flake of Arizona and Marco Rubio of Florida. This is a group that truly spans the ideological spectrum with a plan that includes a series of exquisitely balanced compromises and offers serious hope of movement in the Senate, at least, within a matter of months. Durbin, who was in the middle of the gang of six that brokered a reasonable and courageous plan on deficit reduction, has become a go-to guy to find common ground. Schumer, who was in the middle of the filibuster reform negotiations, is also a key to compromise. McCain was, for many years, the avatar of bipartisan proposals on important and controversial issues from climate change to political reform — if this is a sign of his return to that pivotal role, it is great news. And Graham, up for re-election in South Carolina, has once again shown his courage in the face of immense, career-threatening political pressure.

At the same time, Tom Coburn, R-Okla., another senator who looks to solve problems and not just score partisan points or dig in with uncompromising ideological positions, is trying to find a broad consensus on a gun check plan that could be the centerpiece of some overhaul of gun laws. Immigration and guns are issues that looked six months ago as if they would be impossible to reform, but now it is plausible to imagine both moving forward.

The turnaround on these issues has occurred because of events. For immigration, it was the stunning and unexpected beating Republicans took at the polls: losing the presidency after expecting a comfortable win, losing two seats in the Senate after thinking a GOP majority was a real possibility. The losses opened up Republican eyes to their demographic deficits. For guns, of course, it was the elementary school shooting in Newtown, Conn.

But there are major hurdles ahead, especially in the House. National trends mean little to a least a hundred House Republicans who are more driven by the threat of a primary challenge from the right and who hear mostly from constituents whose attitudes are shaped by the likes of Rush Limbaugh and Glenn Beck, not by Graham, Speaker John A. Boehner or former Florida Gov. Jeb Bush. Turning amnesty from a four-letter word to a seven-letter word is a priority for Graham and Bush. It remains a four-letter word for a lot of GOP primary voters, especially those in the South and Southwest.

Then there is the continuing hurdle of fiscal policy. There is a growing consensus among mainstream economists and business leaders that the debt problem is real but not urgent, that austerity in the short term could lead to a deep recession, akin to Britain now or the United States in 1938. Another relatively modest tranche of deficit reduction, about $1.2 trillion over 10 years, would stabilize our debt-to-gross domestic product ratio at acceptable levels and leave time for constructive reforms in entitlements, the tax structure and other policy areas to achieve robust economic growth in the years ahead that itself would ameliorate any debt issues. But that consensus has entirely eluded the House majority, which is doubling down with a new budget that promises draconian cuts in discretionary domestic spending that would, if enacted, damage areas from food safety to homeland security to research and development and lead to economic upheaval. The sequester alone, if implemented right away, would almost halve projected economic growth in the next year.

Right now, we are headed to a series of mini-confrontations, manufactured games of chicken over debt limit, sequester and shutdowns of government, that could put a crimp in the ability of our political actors to move forward on other issues and could take this encouraging moment on immigration and guns — with the promise of further movement on tax reform, infrastructure development, and a new energy consensus — and send them toward oblivion. So near  . . .  and yet so far from an amazingly productive policy year.

Norman Ornstein is a resident scholar at the American Enterprise Institute.