The only resource Ming wanted for was Silver, as they used it for coinage. At this point in history, it had been proven that a trek across the Pacific was possible. This combined with the Ming's ability to build large ships (as seen with Zheng He's voyages), I'm left with the question, why didn't the Ming attempt to tap into the large quantities of silver in the Americas, as discovered by the Portuguese and the Spanish.
In some ways, I believe you answered your own question! Expeditions of this sort were extraordinarily expensive, requiring the construction and logistics needs of unprecedented scale for the imperial court, which you pointed out was always hurting financially. It's only complicated by a lack of accurate navigational charts for the passage to the Pacific coast of the New World. Therefore, funding such a venture would begin with years of navigational efforts, as it would be hugely inadvisable to attempt to establish mining operations overseas without a known, reliable sea route.
Now, nothing I said there makes the operation an impossibility. If any East Asian element could have pulled off this demanding enterprise, it's the Ming. However, politics always get in the way, especially in Chinese history. It's worth noting that were you, say, a Chinese literati wanting to make this proposal as a petition to the Emperor, you would likely be laughed out of the room. Such a grand, unconventional vision would be viewed as idealistic and extraordinary by the conservative imperial court. The history of Chinese Imperial reformers proves time and time again, (take the Song Dynasty's New Policies or the Qing Dynasty's 100 Days of Reform), indicates that trying to do something new will just about guarantee you an uphill battle against deeply ingrained elements of the landed elite.
But what about Zheng He's "treasure voyages?" These were authorized and relatively successful, so it stands to reason that the Emperor might consider it in that light. Unfortunately, it seems the Yongle Emperor's attitude towards exploration and discovery was a anomaly, as his two successors were both opposed to costly expeditions on principle. Any Ming Emperor following those were in no position to consider such a venture, as they began grappling with increasingly-pressing Mongolian incursions.
So to summarize, the Chinese state at this time lacked the capital necessary to make long-term colonization a natural consideration. Institutional factors and a generally conservative court made the proposal of such an undertaking a feat in and of itself. Finally, any time you're grappling with a question of Chinese history, "mongol invasion" is often a safe answer.