Senate Armed Services Committee Chairman John McCain (R-Ariz.) wants to raise defense spending by $38 billion a year over the caps, which would total $76 billion in additional spending over the two-year span of a deal envisaged by McConnell. McCain has the backing of other defense hawks frustrated by limits on defense spending.

Obama and Democrats say any increases in defense should be matched dollar for dollar with increases to nondefense programs. Meeting that demand could mean a $152 billion increase in discretionary spending over the budget caps for fiscal 2016 and 2017.

Finding a way to pay for a spending increase that large could be difficult, and Republicans don’t want to see a deal that would bust the nation’s budget.

McConnell is telling GOP colleagues that he supports significant reforms to entitlement programs such as Social Security and Medicare, according to Senate sources. Such reforms could pay for increased spending.