Members are usually allowed to propose an unlimited number of amendments to spending bills, but House GOP leaders did not want the bill to get bogged down with controversial proposals that would slow down the bill. As a result, Republicans late Monday allowed a total of just four amendments on the NSA, Syria and Egypt.

During rule debate, Republicans acknowledged that the are not happy with these limitations but said it's better than the alternative of a stalled Defense appropriations bill.

"In perfect honesty, I don't think that this is a perfect rule," Rep. Rich Nugent (R-Fla.) said. "But I know it's the right rule for what we're doing today."

Democrats usually find flaws with GOP rules, and quickly cited the limited amendment rule as a major problem this time around. Rep. James McGovern (D-Mass.) said it is not enough to consider just two amendments on the NSA in the wake of news about the agency's broad program of collecting phone and email data on millions of Americans.

"Isn't it time for Congress to take a serious review of how the law is being implemented, how it is touching and affecting all Americans, and whether any of those laws and their implementation now require changes?" he asked.

Similarly, Rep. Peter WelchPeter Francis WelchMerkley leads Dem lawmakers to border amid migrant policy outcry Lawmakers have sights on middlemen blamed for rising drug costs Dem letter calls for rolling back move targeting drug companies MORE (D-Vt.) said more time is needed to debate possible limitations on funding for the U.S. involvement in Syria's civil war.

"[A]re we going to do our jobs, are we going to be congressmen and women, or are we going to be cowards?" Welch asked. "And it is the coward's path to avoid taking responsibility for a momentous decision that we know at this moment is upon us."

Other members proposed amendments that would prohibit U.S. military aid to Egypt in the wake of what some say was a military coup earlier this month against Egyptian President Mohammed Morsi.

Speaking for the Republicans, Nugent argued that none of these topics were being "swept under the rug," as four amendments will be allowed this week on the three issues. At the same time, he said, the Defense spending bill is not the place to consider radical changes to the NSA program.

"I'm downright furious over what NSA has been doing, and the more I learn about the programs, the more outraged I get," he said. "But to try to change these programs on a DOD appropriations bill, where we can't legislate, isn't the right way about going about fixing something that's broken."

Under the rule, one amendment from Rep. Trey Radel (R-Fla.) will be considered, which would prohibit the use of funds for any military action in Syria that is inconsistent with the War Powers Resolution. But McGovern said that amendment simply restates current law, which requires Congress to authorize military action.

The GOP will also allow a vote on language from Rep. Thomas Massie (R-Ky.) that would block funding for military or paramilitary operations in Egypt.

Two amendments will be considered for the NSA. The first, from Nugent, would prohibit the NSA from targeting U.S. citizens or acquiring or storing phone and Internet data on U.S. citizens. The second, from Rep. Justin AmashJustin AmashGOP rep refutes Trump's account of Sanford attacks: 'People were disgusted' Trump claims Sanford remarks booed by lawmakers were well-received GOP congressman blasts Trump’s attack on Sanford as ‘classless’ MORE (R-Mich.), would completely eliminate the NSA's authority to collect records under the Patriot Act.

Nugent cast his amendment as a middle-ground way of limiting the NSA's authority without ending it. "My amendment would strike a balance between making sure our government has all the necessary tools while keeping our citizens safe, while protecting American civil liberties," he said.

The overall bill would spend about $600 billion in total in 2014, less than 2013. But it still spends more than Democrats would like, and President Obama says it would cut into needed social spending.

On Monday, the White House said Obama would veto the bill unless a budget framework is reached that supports these programs. Congress and the White House are widely expected not to reach this sort of agreement, and instead be forced to reach a continuing resolution for 2014, most likely at the last minute in September.

The rule also allows consideration of the 2014 transportation and housing spending bill, H.R. 2610, which could come up next week. Unlimited amendments will be allowed for that bill.