WASHINGTON — Under pressure to make deeper spending cuts and blindsided by embarrassing floor defeats, House Republican leaders are quickly discovering the limits of control over their ideologically driven and independent-minded new majority.

For the second consecutive day, House Republicans on Wednesday lost a floor vote due to a mini-revolt, this time over a plan to demand a repayment from the United Nations. Earlier in the day, members of the party’s conservative bloc used a closed-door party meeting to push the leadership to go well beyond its plans to trim about $40 billion from domestic spending and foreign aid this year, demanding $100 billion or more.

The spending rebellion came after the House on Tuesday rejected what was expected to be a routine temporary extension of anti-terrorism Patriot Act provisions when Democrats and about two dozen conservative Republicans balked at a fast-track procedure. Republicans, still searching for their footing after assuming control in January, were also forced to pull a trade assistance bill from the floor after conservatives raised objections. They found themselves mediating other internal fights as well.

Speaker John A. Boehner conceded that the fledgling majority was encountering turbulence. “We have been in the majority four weeks,” Mr. Boehner said. “We are not going to be perfect every day.”