The language says, "No government contribution … shall be provided on behalf of an individual who is a Member of Congress, congressional staff, the President, the Vice President, or a political appointee for coverage." Republicans have opposed an Obama administration rule that would allow members and staff to get subsidized health insurance under the exchanges.

The amendment that Republicans hope to pass Monday would also delay the individual insurance mandate for a year. The GOP says that delay is only fair, as President Obama has already delayed the employer mandate to offer health insurance.

Finally, it again funds the government through Dec. 15. The House continues to pass spending resolutions through that date, while Senate Democrats have insisted on a Nov. 15 date.

GOP leaders hope to pass these changes today and send them back to the Senate in the last few hours before a government shutdown.

The Senate, however, has already rejected the measure, and it is unclear whether House Republicans have the votes in their own conference to move their latest proposal. 

The new amendment to the spending bill was made public about an hour after a Senate vote to table other ObamaCare changes that the House passed over the weekend. Those would have delayed ObamaCare for a year and repealed the medical device tax.

The House Rules Committee was expected to meet at 4:15 p.m. to set a rule governing debate and votes on the language.