A fight between Republicans and the White House over a defense spending is expected to come to a fore in over the next few weeks, as Congress advances a defense bill the president has threatened to veto.

Senate and House Armed Services committees are expected to finish combining their respective National Defense Authorization Act (NDAA) bills together as early as this week, Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.), chairman of the Senate panel, said Wednesday at the Heritage Foundation.

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Congress would then have two weeks to pass the final version and send it to the president's desk before a month-long recess break in August.

Although the bill is expected to pass the Republican-majority Congress, but the White House has threatened to veto the bill once it reaches the president's desk, since it authorizes money according to spending caps that he wants Congress to lift.

In addition, the bill would authorize boosting the defense budget by adding money to a war fund that is not subject to the caps, known as sequestration, which the president also opposes.

The White House also opposes a number of other provisions in the bill, including restrictions on transferring Guantanamo Bay detainees to the U.S., although the Senate bill includes a pathway for it.

President Obama reiterated his veto threat during a visit to the Pentagon earlier this month, and McCain said he's "very much afraid" the president will veto the bill, forcing Congress to start over the process.

McCain said he spoke with Defense Secretary Ash Carter Wednesday morning, and said he was "very disappointed" that Carter supports a presidential veto.

He also said the president should be targeting defense spending bills, which actually appropriate money, not the defense authorization bills, which authorizes Pentagon programs and spending.

“The NDAA is an ambitious policy bill, but there is one issue this bill ultimately cannot solve: the arbitrary caps on defense spending and the mindless mechanism of sequestration created by the Budget Control Act of 2011," he said.

Senate Democrats have vowed to block any spending bills from being passed, until Republicans sit down and discuss how to lift the caps on defense and non-defense spending.

If a resolution is not reached before the August recess, Congress would only have three weeks before a new fiscal year begins in October.

If spending bills are not passed and signed into law by then, Congress would either have to shut down the government or pass short-term spending measures known as continuing resolutions.

A continuing resolution would mean an extension of 2015 defense spending levels, and the prevention of any new spending or programs, and possibly pay raises for troops if there's no resolution by January.

McCain touted the many reforms the defense bill contained, such as reform of the Pentagon's weapons-buying and military retirement systems.

"To prepare our military to confront our present and future national security challenges, we must champion the cause of defense reform, rigorously root out Pentagon waste, and invest in modernization and next-generation technologies to maintain our military technological advantage," he said.

“The National Defense Authorization Act that passed the Senate last month is an important first step towards accomplishing those goals," he said.