House Majority Leader Eric Cantor (R-Va.) has been saying for weeks that Medicare reforms may be tied to the vote, while Sen. Jim DeMint (R-SC) has expressed an interest in using the debt-ceiling vote as leverage to approve a balanced budget amendment.
Complicating the math are centrist Democrats like Sen. Joe Manchin (D-W.Va.), who said he can support spending caps in the context of a debt ceiling vote. If enough Democrats end up favoring something other than a clean debt limit increase, political leaders from both parties will need to thread a very narrow needle to find a solution or risk not a shutdown, but the "full faith and credit" of the United States.
With that as a background, House Republicans will be looking to continue their attack on the healthcare law, and will also start work on two bills aimed at boosting U.S. oil exploration.
Below is a more detailed look at the week ahead:
The House meets at 2 p.m. to take up two bills under a suspension of the rules. The first is H.R. 1423, which would name a post office in Oklahoma, and the second is H.R. 362, which would name a courthouse in Midland, Texas after Presidents George H.W. Bush and George W. Bush.
The Senate also returns Monday and is expected to hold at least one vote on a non-controversial judicial nominee.
The House meets at noon to take up H.R. 1213, which would end federal funds for state health insurance exchanges, and H.R. 1214, which would end federal funds for school-based health centers. Both bills would repeal programs established in last year's healthcare law. The House Rules Committee is scheduled to approve rules for these bills on Monday.
The Senate may resume work on the small business bill, S. 493, for the rest of the week.
The House meets at noon to consider H.R. 3, which would permanently ban taxpayer-funded abortions. A rule for this bill is expected Monday.
The House meets at 9 a.m. to take up legislation restarting offshore lease sales, H.R. 1230. The House may also begin work on H.R. 1229, which would require action on Gulf of Mexico drilling permit applications. Rules for both of these bills should be approved by Wednesday night by the Rules Committee.
The House is not in session.