House Republican leaders moved Thursday to potentially keep members on call throughout the month of August in order to pass a border bill sometime in the coming days and weeks, frustrating members who were looking to escape Thursday afternoon for a five-week recess.

As a start, Republicans will meet Friday morning to continue their discussions on how to pass a border measure, after many Republicans said they had to have a vote on fixing the crisis at the southern U.S. border. Just hours ago, GOP leaders pulled two border bills after failing to get enough Republican votes.

House Rules Committee Chairman Pete Sessions, R-Texas, left, oversaw the approval of a rule that could allow the House to vote any time in August on border legislation. (AP Photo/J. Scott Applewhite)

In the hopes that some agreement can be reached on a border bill in the coming days or weeks, the House Rules Committee approved a rule late Thursday that would allow the House to move more quickly to pass the legislation. The rule governing consideration of any new bill allows Republicans to call members back to work at any time through early September — the rule is expected to be approved by the House Friday morning.

“I want to provide us with the maximum amount of flexibility,” Rules Committee Chairman Pete Sessions (R-Texas) said the possibility of votes deep into August.

After leaders pulled the two border bills, incoming House Majority Leader Kevin McCarthy (R-Calif.) warned members that more votes could happen later Thursday night. When asked when he might know for sure, he said he would know “late this afternoon,” prompting grumbling among members.

Soon afterwards, Republicans began a meeting that lasted for nearly two hours, in which most Republicans favored staying in session until some vote could be held before members leave for the recess.

But the decision to keep the House working may end up being mostly symbolic. Even if the House can pass a bill that House Republicans can support, it’s likely to be rejected by the Democratic Senate.

Democratic leaders have indicated they would likely replace any House bill with language that Republicans will find objectionable. Senate Majority Leader Harry Reid (D-Nev.) has said the Senate might add the comprehensive immigration reform bill, which House Speaker John Boehner (R-Ohio) has already said is a non-starter in the House.

One of the bills that Republicans tried to call up today would provide $659 million in funding to increase the capacity of border officials to deal with the flood of illegal child immigrants. It also would have changed current law to allow Central American children to be processed in a more expedited way.

Another bill would block President Barack Obama from expanding an amnesty program for millions of illegal immigrants.