UPDATE 2:08 p.m. ET: Republicans have only held the majority in the House of Representatives for six weeks. But the GOP has now lost two of its first 28 votes.

One day after a bungling a vote that would have reauthorized provisions of the Patriot Act, a coalition of Democrats and Republicans upended a second bill Wednesday.

Wednesday’s legislation would have refunded some $180 million to the U.S. Treasury that the government paid to the U.N. Tax Equilization Fund (TEF). Some of that money was devoted to securing the U.N. in New York and was requested by the New York Police Department.

Republicans brought the U.N. bill to the floor under an expedited procedure that requires a two-thirds vote to pass.

A majority of House members voted in favor of ordering the refund as the final tally was 259 to 169.

However, with 428 members voting, the House needed 286 votes to approve the package.

In a Tuesday night stunner, the House rejected a renewal of key provisions in the Patriot Act after the new GOP majority also brought the legislation to the floor under a provision entailing a two-thirds vote. That measure fell seven votes short of the two-thirds requirement.

PREVIOUS STORY: House Anticipates Potential Second Failed Vote in Less than 24 Hours

Less than 24 hours after suffering a major embarrassment by failing to renew key provisions of the Patriot Act, the House Republican majority could face another potential legislative blunder.

And buoyed by last night's unexpected victory on the Patriot Act, many House Democrats are poised to give the GOP enough rope today.

On the floor is one of the GOP's "YouCut" votes, where House Majority Leader Eric Cantor, R-Va., solicits people to cast votes on the web to target a particular program.

This week's "winner" (or loser, depending on who you ask), is a plan to require the United Nations to return nearly $180 million that the U.S. has paid into the U.N.'s Tax Equilization Fund (TEF). The U.N, is supposed to route some of that money to the Americans who work there to help cover the cost of taxes they pay on their salaries. Non-Americans employed by the U.N. don't pay taxes on their salaries in their native countries.

The U.S. has overpaid into the fund and now the U.N. is devoting some of the money to bolster security at headquarters in New York.

YouCut efforts have been unpopular with most Democrats, sometimes decried as "show votes." House Minority Whip Steny Hoyer, D-Md., said Wednesday that this particular vote would "have no impact on the deficit. It's rhetoric."

Now here's the rub: The U.N. vote, like last night's failed Patriot Act vote, will be treated as a "suspension" bill. Under "suspension" procedures, the House "suspends" the regular rules which require a simple majority vote to pass a bill. The trade-off is an expedited process to get a bill to the floor followed by an abbreviated debate. For the fast track maneuver, the House raises the threshold to approve a bill to two-thirds rather than the simple majority. Traditionally, the suspension process is reserved for non-controversial measures that have little trouble gathering the support of two-thirds of those voting.

Democrats know that going into today's vote and could help spell another defeat for Republicans on the floor.

However, there is some gamesmanship unfolding on both sides.

Republicans blamed Democrats last night for not voting in favor of the Patriot Act Tuesday night. That vote caught everyone by surprise and fell short of the two-thirds requirement. Still, 26 Republicans voted against the bill. But Republicans are ready to again blame Democrats if this bill implodes, too.

"House Republicans are standing with the American people in their desire to cut spending in order to reduce barriers to job creation and economic growth," said Erica Elliott, a spokeswoman for House Majority Whip Kevin McCarthy, R-Calif. "If Democrats want to play partisan politics with $180 million in taxpayer dollars, I think that clearly shows they didn't learn any lessons from this fall."

Meantime, Democrats are prepared to try to embarrass Republicans if one their own bills fails for the second time in as many days. Sources indicate to FOX that many Democrats are prepared to vote against the package.

On the U.N. bill, the New York Police Department has asked for the money to help provide security and New York Mayor Michael Bloomberg is also said to be pushing for the money.

On Tuesday, Republicans also yanked a trade bill from the floor once it was obvious it didn't have the votes to pass.

House Speaker John Boehner, R-Ohio, tried to deflect criticism about how the GOP managed the Patriot Act legislation.

"We're not going to be perfect every day," Boehner said. "We've been in the majority four weeks."

Meantime, Democrats were happy to pile on to the GOP.

"I think their party is divided," Hoyer said.