The Republican leadership has postponed a second vote on a high-profile piece of legislation, as it works to establish a clear message on key issues such as abortion and immigration leading up to the 2016 presidential election.

House leaders indefinitely postponed a vote on a border security bill, Secure Our Borders First Act (HR 399), which seeks to penalize the Department of Homeland Security (DHS) if it fails to stop all illegal border crossings in five years. The postponement came less than a week after leadership angered conservatives by delaying a vote on a controversial abortion bill at the last minute.

Asked about such splits at a news conference on Tuesday, the House speaker, John Boehner, said: “There have been a couple stumbles.”

Democrats and some conservatives have criticised the border security bill for being unrealistic. Conservatives are also critical of the bill for failing to aggressively challenge President Barack Obama’s executive action on immigration, which he announced in November.

Republicans were pushing for a Wednesday vote on the bill, because Congress has a shortened schedule this week while the Democrats stage their annual retreat. The weather was relatively calm in DC overnight, but concerns over nationwide travel problems caused by winter storms prompted the Republican leadership to indefinitely postpone the vote.

Tensions over the border security bill have again exposed fissures in the Republican party, after last week’s female representative-led rebellion that caused it to ditch an abortion bill the night before a scheduled vote. That decision exposed rank-and-file dissent and frustrated the GOP’s most conservative members on the eve of the country’s largest anti-choice demonstration.

Mississippi representative Bennie Thompson, the House homeland security committee’s top-ranking Democrat, said the weather was a convenient excuse for House leadership to pull the vote on the immigration bill.

“They can blame inclement weather all they want, but we all know that it was the storm clouds over this bill and its murky prospects that are the real drivers,” he said. “Interestingly, even the most extreme rightwing elements of the House Republican conference, which the bill was written for, could not get on board with this legislation.”

Representative Mike McCaul, of Texas, is chairman of the House homeland security committee, where the Secure Our Borders First Act passed last week along party lines. “For God’s sakes, if we can’t unite around border security, what can we unite around?” he said during those discussions.

McCaul and other supporters of the bill argue that it is the first step in a series of legislative efforts to dismantle Obama’s executive action on immigration and that it could lay the foundation for Republican-led reform.

Jessica Vaughan, director of policy studies at the Center for Immigration Studies, a conservative thinktank, said the Secure Our Borders First Act was a “token bill” and added that the party should instead be making moves for harsher penalties on people who illegally cross the border.

“If the rest of Congress goes along, they will have squandered the political momentum gained from their response to the border surge crisis – not to mention wasting an opportunity to restore some integrity to our immigration laws and their sole authority to craft them,” Vaughan wrote in a blogpost criticizing the bill.

The White House position is clear. The homeland security secretary, Jeh Johnson, said on Friday the bill was “extreme to the point of being unworkable”. He also said the bill undermined the DHS and “politicizes tactical decisions”.

House Democrats have echoed such statements and are especially critical of a provision that calls for penalties to be enacted against the DHS if it fails to put the border under “operational control” in five years. The bill defines “operational control” as blocking or turning back all attempted border crossings.

Under such penalties, politically appointed DHS officials would not be allowed to travel in government vehicles, would not be reimbursed for nonessential travel and would not be eligible for bonuses or pay increases.

Along with the “operational control requirement”, the bill seeks to add and replace fencing along the border, build new roads and create more bases for border patrol agents.

To scale back Obama’s immigration reforms, the GOP has also attached amendments to a DHS funding bill. The White House has said it will veto legislation containing such amendments.

As the 27 February DHS budget deadline creeps closer, pressure is on for the Republicans to take a clear stance on immigration. With the presidential election approaching, the party must work not to alienate the powerful Latino voter base.

In the Republicans’ State of the Union rebuttal last week, Representative Carlos Curbelo, of Florida, strayed from the English-version of the speech, calling for immigration reform in the party’s Spanish language address.