Supporters say the bank helps level the playing field for U.S. companies against competitors in Europe and China, who get significant help from their governments. Detractors call the bank crony capitalism that mostly helps big business.
But really, as Cruz's speech showed Friday, the bank has become a proxy battle for something else entirely: Government's place in business. And it appears those who want government out of business have won this battle -- for now.
Here's everything you need to know about the debate.
First, help me understand exactly what the bank does
During the Great Depression, Franklin Delano Roosevelt created the bank. Its mission was to generate U.S. jobs by supporting American companies' business abroad.
But the bank's job is not to hold up every company that wants to expand overseas. It finances less than 2 percent of exports, according to the Wall Street Journal. The bank only steps in when private insurers don't want to cover the cost of a risky investment -- for example, the U.S. building a railroad in a politically unstable country.
General Electric's head, Jeffrey Immelt, says that layer of support is crucial for helping his company win competitive infrastructure contracts abroad. Most companies in developed countries enjoy similar support from their governments -- if not more, in the case of communist China. If GE loses Ex-Im Bank support, Immelt has threatened to ship some jobs overseas to keep costs down so he could still compete for those contracts.
"We’re fighting an economic war for exports," he said in a recent speech.
And if life without the Ex-Im Bank would be tough for GE, business leaders like the Chamber of Commerce say, imagine what will happen to smaller companies. A lot of bad things, Don Nelson, president of the small business ProGague Technologies, told Politico.
"We won't be able to export anymore," he said.
So, who would be against such a seemingly do-good agency?
Tea party and libertarian groups are not a fan. The bank represents all that is wrong with America, they argue; it's crony capitalism that props up the wealthy corporations with taxpayer money. They point to the fact that 87 percent of the bank's loan guarantees go to Boeing, Caterpillar and GE. The Export-Import Bank might as well be called"The Boeing Bank," they say.
"It is the purest form of corporate welfare," Dan Holler of the conservative group Heritage Action for America told the AP.
My colleague, Philip Bump, wrote Cruz's speech Friday was perfectly timed to fit the endorsement of prominent conservative celebrity Brent Bozell, and the "Washington cartel" and corporate welfare have been a major theme of his campaign.
Libertarians say the government agency also unnecessarily politicizes what should be free international markets.
"The trade practices of other nations do not provide a justification for corporate welfare at home," Michael R. Strain of the conservative American Enterprise Institute wrote in The Washington Post last year.
In some cases, the bank gives loans directly to foreign companies to help them buy U.S. exports, like a $120 million loan in 1996 to a Chinese nuclear corporation. Not the best optics.
Do most Republicans dislike the bank, then?
No, not really. In fact, a majority of Congress on both sides of the aisle has signaled support for the bank, including "dozens" of House Republicans, the Wall Street Journal said.
Pro-business and Republican-leaning groups like the Chamber of Commerce are lobbying heavily on Capitol Hill to keep it. And they're surprised that this is even an issue they have to lobby so hard for: The relatively obscure bank has always had its critics, but it's never risen to such a prominent debate before.
Politico notes it's survived 81 years, 13 presidents and 16 reauthorizations.
So why are we here now?
There's one really important person who has sided with opponents of the Ex-Im Bank: Senate Majority Leader Mitch McConnell (R-Ky.). He controls what bills come to the floor, and he's responsible for letting Tuesday's bank expiration date go by without a vote. (He promises a vote on the bank sometime, though, likely when Congress returns from its Fourth of July recess next week.)
The House's No. 2 and No.3 Republicans also have opposed the bank, and Speaker John A. Boehner (R-Ohio) has stayed mum -- a sign he's torn between competing factions in his party.
There are other really powerful people who just happen to oppose the bank, too: Billionaire GOP donors Charles and David Koch, who according to The Washington Post's Matea Gold and Tom Hamburger, are funding "a fierce assault" on the bank.
What will happen if Congress lets the bank expire?
Since Congress let the bank's June reauthorization date come and go without acting, the bank is allowed to follow through on the $112 billion in loans that it's already agreed to, but it won't be allowed to start up any new ones.
That will throw at least a little wrench in the U.S. business community, but its impact is more notable in the political realm. The bank's (possibly temporary) expiration is a huge win for the right wing of the Republican Party like Cruz & co. They've succeeded in convincing the highest levels of government that the bank is a symbol of big government and has to go. The war on the Ex-Im Bank is the beginning of the end for government welfare programs that don't abide by the free market, they hope.
Again, conservative economist Michael Strain: "My hope is that the Battle of Ex-Im will be the first in a long war that will unwind other instances of corporate welfare and crony capitalism. For its symbolic importance alone, the bank should not be reauthorized."
The bank expiring is also a blow to the business lobby, whose power on Capitol Hill appears diminished in this fight. They are arguably the biggest losers in all of this, because not long ago they dominated the Republican Party.
Every day that ticks by past the reauthorization deadline enforces all of these new political realities. Warned Sen. Dick Durbin (D-Ill.):
“Once it closes shop, I think it becomes increasingly difficult to revive it."
[This post has been updated]