Immigration petition hits 204 as new Republican signs on
© Greg Nash

Another House Republican has signed on to the discharge petition that would force a series of votes on immigration that GOP leaders are seeking to avoid, bringing the number of signatories to 204.

Rep. Erik PaulsenErik Philip PaulsenPaul Ryan to campaign for 25 vulnerable House Republicans How America’s urban-rural divide is changing the Democratic Party The bipartisan PACT Act would ensure access to life-saving bone marrow transplants for Medicare beneficiaries MORE's (R-Minn.) signature means the petitioners need just 14 more signers to force a series of votes on immigration legislation that would offer shelter to "Dreamers," immigrants who came to the United States illegally as children.

Paulsen, a top Democratic target in the midterm elections who represents a district Hillary ClintonHillary Diane Rodham ClintonHillicon Valley: Bolton tells Russians 2016 meddling had little effect | Facebook eyes major cyber firm | Saudi site gets hacked | Softbank in spotlight over Saudi money | YouTube fights EU 'meme ban' proposal Dems lower expectations for 'blue wave' Election Countdown: Takeaways from heated Florida governor's debate | DNC chief pushes back on 'blue wave' talk | Manchin faces progressive backlash | Trump heads to Houston rally | Obama in Las Vegas | Signs of huge midterm turnout MORE won in 2016, is the 21st Republican to sign the petition.

Twenty-five GOP signatures are needed if every Democrat in the House backs the petition, meaning the petitioners may just need another four signatures to reach their goal.

GOP leaders have pressed lawmakers not to sign the discharge petition, which would allow a minority of Republicans working with Democrats to control the floor.

House Majority Leader Kevin McCarthyKevin Owen McCarthyGOP lawmaker proposes legislative maneuver to fund Trump's border wall Maxine Waters gets company in new GOP line of attack The Hill's Morning Report — Presented by the Coalition for Affordable Prescription Drugs — GOP faces ‘green wave’ in final stretch to the midterms MORE (R-Calif.) has warned members of his conference it could have negative implications during the midterm election cycle.

Top Republicans have recently floated an alternative plan to hold a series of immigration votes on bills picked by House GOP leadership the week of June 17, according to sources familiar with the discussions.

Under the Queen of the Hill rule, the conservative-backed bill by Reps. Bob GoodlatteRobert (Bob) William GoodlatteConservatives fume over format of upcoming Rosenstein interview Rosenstein to appear for House interview next week Fusion GPS co-founder pleads the Fifth following House GOP subpoena MORE (R-Va.) and Michael McCaulMichael Thomas McCaulSenate passes key cyber bill cementing cybersecurity agency at DHS Hillicon Valley: Trump stuns with election interference claim against China | FCC limits fees for 5G | Uber reaches 8M settlement over breach | Fox sells Sky stake to Comcast | House passes bills to fix cyber vulnerabilities Sessions calls on former colleagues to send drone legislation to Trump's desk MORE (R-Texas), the bipartisan USA Act, the Dream Act and a bill of Speaker Paul RyanPaul Davis RyanElection Countdown: Takeaways from heated Florida governor's debate | DNC chief pushes back on 'blue wave' talk | Manchin faces progressive backlash | Trump heads to Houston rally | Obama in Las Vegas | Signs of huge midterm turnout Will the Federal Reserve make a mistake by shifting to inflation? Sanders: Democrats ‘absolutely’ have chance to win back rural America  MORE’s (R-Wis.) choosing would come to the floor. The measure that receives the most votes over the 218 threshold would then be sent to the Senate.

House GOP leadership has promised members of the conservative House Freedom Caucus a vote on the Goodlatte-McCaul legislation in June. Members of the caucus are hoping a stand-alone vote on the White House-backed measure would kill the discharge petition.

Rep. Jeff DenhamJeffrey (Jeff) John DenhamDems target small cluster of states in battle for House Poll: Dems lead in 5 critical California House seats Dems announce third-quarter fundraising bonanza MORE (R-Calif.), a leader on the discharge petiiton, wants a single rule to set up all the bills so that the Freedom Caucus can’t tank the rule for the moderate-backed bill spearheaded by Reps. Will HurdWilliam Ballard HurdElection Countdown: Takeaways from heated Florida governor's debate | DNC chief pushes back on 'blue wave' talk | Manchin faces progressive backlash | Trump heads to Houston rally | Obama in Las Vegas | Signs of huge midterm turnout O'Rourke's rise raises hopes for Texas Dems down ballot Election Countdown: Dems outraise GOP in final stretch | 2018 midterms already most expensive in history | What to watch in second Cruz-O'Rourke debate | Trump raises 0M for reelection | Why Dems fear Avenatti's approach MORE (R-Texas) and Pete AguilarPeter (Pete) Ray AguilarHispanic Dems want answers on detention of immigrant minors Aguilar launches bid for Democratic leadership position Koch group launches digital ads in tight Texas House race MORE (D-Calif.).

Freedom Caucus Chairman Mark MeadowsMark Randall MeadowsConservatives fume over format of upcoming Rosenstein interview Farm bill negotiators should take advantage of the moment Conservative rep slams Rosenstein's 'conflicts of interest' MORE (R-N.C.) called on leadership to do everything in their power to stop the discharge petition from moving forward, adding he believes bringing up the Goodlatte bill is the easiest way to derail moderates' efforts.

"When I voted against a rule, they threatened to take away all travel, they threatened to take away any NRCC contributions," he told reporters Monday evening, referring to the House Republicans' campaign arm, the National Republican Congressional Committee. "Most of those people that were on the discharge petition are much closer to leadership than members of the Freedom Caucus — so I don't see them voting against the rule."

Meadows said he wouldn't be supportive of bringing up a rule that also includes the legislation being worked on by Denham, arguing he doesn't know what the final product will look like.

"I think it's two separate votes. I mean, the truth of the matter is ... we'll vote on the Goodlatte bill as it was promised some seven months ago," he said. "Let's vote on that, and then if we know the parameters of the other bill with Mr. Denham or anybody else, I don't envision any bloc of votes voting against the rule from our side."

The North Carolina lawmaker said Republicans need to prove to the American people Goodlatte doesn't have the 218 votes needed to send his legislation to the upper chamber before looking at alternatives.

"I guess the question is if that's the only bus leaving the station, how many people actually vote for the Goodlatte bill?" he asked. "And I can tell you there are discussions going on right now on how you modify the Goodlatte bill to get to 218."

Melanie Zanona contributed to this report.