The bond auction's success was attributed to investor expectations that Spain will eventually ask for help from the ECB's new bond-buying program. (Read More: Spain Faces ‘Surreal’ Situation, Despite Strong Bond Auction.)

Spain hasn't committed to requesting such a bailout, but Spanish executives want the government to do so soon. They're worried that the lower rates will be short-lived if the country does not turn to the ECB for help.

In private conversations, these executives expressed frustration at the cost of borrowing, simply because their business is headquartered in Spain, even if most of their revenue comes from outside the country.

One of the few who would speak on the record is Carlos Espinosa de los Monteros, a leading light of corporate Spain, who is now working for the Spanish government.

In an exclusive interview with CNBC, Espinosa de los Monteros said unequivocally that Spain should turn to the ECB for help. (Read More: Spain's Prime Minister May Seek Help from ECB.)

“At this moment our companies, our firms, are paying higher interest than our competitors and we need to have the same weapons," he said. "We need to pay similar rates of interest and in order to do that we need this help from the central bank.”

Espinosa de los Monteros currently sits on the board of Inditex, the company behind the mega-brand Zara. Espinosa chaired the board of Mercedes Benz Spain until 2009, and the board of Spanish airline Iberia before that. He holds an MBA from Northwestern and just last year was appointed by the Ministry of the Exterior to improve “Brand Spain.”

As part of that effort, Espinosa said Spain is restructuring its economy in order to become more competitive.

“I can affirm very strongly is that what we are doing in Spain is something that was never done before," he said. "That there’s a huge effort to make our laws more competitive, our companies can have a better life in terms of the legal conditions. And this is a process that’s going to produce results in the medium term, hopefully in the short-term also.”

One of the biggest changes is a new labor law that went into effect in February, which gives companies more flexibility to lay off workers and/or lower wages. These changes have led to large protests across the country.

In response to the demonstrations, Espinosa said: “The people in the streets are always a minority. People have discovered the right of expression, something that wasn’t so common in Spain for years. They have their own opinions and they are free to make their opinions known for other people, and they have to be respected. Although most Spaniards would not agree with their points of view.”

And while protestors do not like the new laws, businesses leaders say it will actually lead to more hiring.

Another well-known executive, Jesus Sainz, who now heads up Madrid’s office of business development, told CNBC the new labor law is one of the reasons that Las Vegas Sands finally committed to developing a large casino and convention project in Spain. Announced just two week ago, EuroVegas, is expected to require $35 billion in investments.

If and when completed, it will be the largest private infrastructure project in the history of Europe. More importantly, it will create more than 200,000 jobs, Sainz said, which would reduce unemployment in Madrid by 50 percent.

The mere announcement by ECB President Mario Draghi two weeks ago that he would be willing to buy countries’ debt in the secondary market pushed interest rates lower across Europe. (Read More: ECB to Buy Sovereign Bonds in New Program to Save Euro.)

And on Thursday, Spain borrowed 4.8 billion euros ($6.26 billion) at a rate of 5.66 percent, the lowest level since January. And sources told Dow Jones that 705 of the buyers were foreigners.

Investors could very well be buying Spanish debt because they expect the ECB to be a buyer as well. However, the government of Spain must explicitly ask for the help, and so far they have not.

—By CNBC's Michelle Caruso-Cabrera

@MCaruso_Cabrera