US Senator Patty Murray (D-WA) hurries out the door just off the Senate floor immediately following votes on Department of Homeland Security funding at the Capitol in Washington, February 27, 2015. Senators departed Washington for the weekend after approving a full-year, $39.7-billion funding measure for Homeland Security that excludes restrictions on Obama's immigration order that House Republicans had been demanding. [Photo/Agencies]

"It's very possible that come September, you could face this again," said conservative Republican Representative Joe Pitts of Pennsylvania, when asked about debt and budget fights ahead.

For small-government Tea Party activists looking to flex their muscles after November's election victory, any attempt to borrow beyond the $18 trillion national debt will be a red flag. Congress also faces a Sept. 30 deadline for passing spending bills that are certain to add to the $18 trillion debt.

Unlike the upcoming debt limit and budget issues, the DHS battle was not about government spending, but about Obama's recent executive actions to suspend the threat of deportation for 4.7 million illegal immigrants.

Still, Trent Lott, a former Senate Republican leader, said some congressional Republicans will not be able to resist further confrontations, especially over spending bills.

"I must say, there are going to be battles for the next two years trying to rein in Obama's excesses with executive power and regulations," Lott said.

More executive actions are expected from Obama in environmental and other controversial areas. That could mean that clashes will intensify, with many conservatives still seeing spending power as their strongest leverage.

Some of them say pressing the immigration fight is part of a non-negotiable duty for Congress to defend the Constitution. They say Obama took steps to change immigration policy that only Congress has the authority to carry out.

"This is not about immigration. This is about whether or not the president has the ability to unilaterally run this country, Representative Austin Scott of Georgia said in House floor debate on Friday.

The Obama administration counters that its unilateral action on immigration, after years of watching House Republicans block legislation, and has many presidential precedents.

Many Republicans are concerned that such fights are an election liability and undermine the party's ability to demonstrate it can govern responsibly. However, similar concerns have been aired with each successive battle.

Republican Senator Mark Kirk, who could face a tough re-election in 2016, told Reuters that his party needs to change.

Referring to the DHS fight, the Illinois senator said: "I would say that this battle should be the end of the strategy of attaching whatever you're upset at the president about to a vital piece of government."