Some Republican senators have complained that Democrats are rushing the bill since new language was added just last week.

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Later Monday, the Senate will vote on whether to end debate on a substitute amendment from Senate Judiciary Committee Chairman Patrick LeahyPatrick Joseph LeahyMaxine Waters to Sessions: 'Time to go back to the plantation' Franken has 'a lot of questions' for Sessions on Russia contacts Senate Dems demand Sessions testify after Papadopoulos plea deal MORE (D-Vt.). His amendment included the “border surge” language from GOP Sens. Bob CorkerRobert (Bob) Phillips CorkerTax Foundation: Senate reform bill would cost 6B GOP senators raise concerns over tax plan Dem House candidate apologizes for saying it 'shouldn't take brain cancer' for McCain to show courage MORE (Tenn.) and John HoevenJohn Henry HoevenSenate tax plan may delay corporate rate cut by one year: report Pence to visit ICBM base The Hill's Whip List: Republicans try again on ObamaCare repeal MORE (N.D.), which requires 700 miles of Southern border fencing and hiring of 20,000 more border patrol agents before immigrants can apply for green cards.

Adoption of that amendment is viewed as critical to attracting more Republican support for final passage, which the bill’s authors want in order to put more pressure on the House to take up the legislation.

A vote to end debate on the whole bill will likely come Wednesday morning or Tuesday evening.

The Senate bill would create a pathway to citizenship for illegal immigrants already in the country, toughen border security, create a guest-worker program and boost high-skilled immigration.