BUENOS AIRES, Jan 10 (Reuters) - Argentina's markets, which soared after President Javier Milei took office a month ago, are now giving the libertarian leader a dose of reality, with bond prices slipping, the peso weakening again and investors wary of the government's new debt auctions.

The splash of cold water from investors after an initial honeymoon underscores the huge challenge facing Milei as he looks to tamp down inflation heading towards 200%, head off social unrest, rebuild depleted reserves and rescue a $44 billion program with the International Monetary Fund (IMF).

He also faces push-back to his 'omnibus' reform bill aiming to privatize state entities and raising taxes in Congress, where his libertarian coalition is well short of a majority. A decree deregulating the economy has also faced legal hurdles.

"Reality is hitting him in his face," said local financial analyst Marcelo Rojas. "His intentions are good, but that is not enough and that's what we're starting to see."

The country's sovereign bond prices have started to slip after a strong run since Milei's win in mid-November. A country risk index has hit the highest level in seven weeks, and a "Bopreal" bond aimed at importers has failed to find buyers.

Meanwhile, the gap between the official peso-dollar exchange rate and parallel rates - used by many to get around tight capital controls - is widening again after a huge devaluation in December had narrowed it significantly.

"The government is beginning to face its first obstacles. Its lack of political muscle is now more evident: the bonus for importers failed to take off and the exchange gap has widened again earlier than expected," brokerage Cohen said in a note.

It added Milei's decree and reform bill did not look promising unless the president was willing to compromise.

The central bank has, however, built up almost $4 billion in foreign currency reserves since Milei took office, and the local S&P Merval stock index remains up strongly, with state oil firm YPF having been buoyed by privatization talk.

EYES ON INFLATION

All eyes meanwhile are on the economy, with inflation expected to have clocked in at nearly 30% in December and topped 200% last year. Two-fifths of people are already in poverty.

The country, a major grains exporter, is also racing to revive its huge IMF deal, with talks in Buenos Aires over the last week aiming to unlock the seventh review of the program and some $3.3 billion of funds.

Economist Aldo Abram from the Libertad y Progreso Foundation said the market outlook rested heavily on Milei's success or failure with his reforms.

"The bad thing is that, as is happening now, all the news that could slow down the government's progress will create a further fall in demand for pesos, putting us closer to hyperinflation," Abram said.

"On the other hand, everything that leads to confirming the change of course will encourage preference for local assets, moving us away from crisis."

(Reporting by Jorge Otaola; Editing by Adam Jourdan and Nick Zieminski)