As bids in an unexpectedly hot auction for U.S. wireless spectrum topped $36 billion Monday, carriers went about issuing billions of dollars in debt for when the time comes to pay for it.

Verizon Communications Inc. on Monday outlined plans to raise 2.4 billion euros in debt citing spectrum as a use of the funds. Smaller carrier U.S. Cellular Corp. said it plans to raise up to $500 million in new debt to pay for spectrum purchases among other purposes. Chief Executive Kenneth Meyers said the company's existing financial resources, though strong, "may not be sufficient to fund all of the long-term investments that the company is making."

The moves came after AT&T Inc. last week offered 3.8 billion euros of bonds earmarked for general corporate purposes, and satellite broadcaster Dish Network Corp., which registered for the auction, wrapped up a $2 billion debt offering.

Companies seeking a piece of the new spectrum will need to line up extra cash in advance. Winning bidders will owe a 20% down payment on their new licenses by Jan. 7 or 10 days after the auction ends, whichever is latest. Final payments are due the later of Jan. 21 or 10 days after down payments come due.

The now-record auction has turned into a surprise windfall for the government, as carriers aggressively bid to line up the airwaves they'll need to cover booming demand for wireless Internet as Americans watch more videos, stream more music and spend more time surfing the Web on their phones and tablets.

AT&T's shares slid 1.6% to $34.70 Monday, as investors braced for more spending. Verizon's shares fell 1.4% to $49.50. Shares in Dish, which owns licenses for a swath of spectrum similar to what the government is offering, climbed 3.2% to $76.05.

"You have more spectrum, and you need to spend more to use the spectrum that you've spent billions to buy," said Wells Fargo analyst Jennifer Fritzsche said. "Something's got to give."

Write to Drew FitzGerald at andrew.fitzgerald@wsj.com

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